Eric Knopf

Efficient Modelling of Rotor-Blade Interaction Using Substructuring

For safe rotor operation it is important to predict the torsional natural frequencies of the full rotor arrangement and not only of its components. The system’s natural frequencies are typically speed-dependent if rotor and blade vibrations are coupled. In this contribution we focus on the torsional rotor-blade interaction, the coupling between torsional vibrations of the shaft and bending vibrations of blade rows attached to the shaft. During the design of a turbine shaft train, rotor blades are modelled using 3D finite elements due to its complex geometry and resulting vibration modes. This kind of model incorporates typically centrifugal loading due to the rotor rotation as well as contact modelling at the rotor-blade interface. Employing the method of substructuring enables to translate any complex blade which is modelled using 3D finite elements with thousands of physical degrees of freedom into a bunch of models with a single modal degree of freedom. Natural frequencies and modal masses are assigned to each modal degree of freedom representing the blade vibrations. These single degree of freedom models are coupled via so-called modal effective moments of inertia to the rotor shaft model. The resulting model resembles the rotor-blade interaction in all its details from the rotor point of view. The efficiency of this process is two-fold. On one hand, the resulting model size of the full rotor dynamic model becomes small and simple enough to allow elaborate parametric studies and design optimisations. On the other hand, translating the complex 3D blade model into a bunch of single degrees of freedom oscillators is extracted straightforwardly from standard output of commercial finite element software packages like Abaqus or Ansys.

Consideration of Complex Support Structure Dynamics in Rotordynamic Assessments

In rotordynamic analyses, support structures are commonly represented by lumped mass systems (single-degree-of-freedom, SDOF). This representation is easy to implement using standard rotordynamic tools. However, in reality the dynamic behaviour of the support structure (e.g. pedestals, casings, foundations) are in general much more complex. Only a multi-degree-of-freedom (MDOF) representation provides modelling close to reality.For many applications the dynamic behaviour of the support structure significantly influences the rotordynamic characteristics of the shaft train and therefore needs to be included in the assessment. Due to this impact, a good quality of the dynamic model used for the support structure is imperative. Regarding the rotor itself, the modelling is well understood and the prediction quality is excellent, not least due to the jointless welded rotor design.Numerous theoretical approaches exist for considering the complex dynamic behaviour of the support structure, all coming along with both drawbacks and opportunities. By discussing the characteristics of established approaches for modelling the support structure, the paper particularly presents an advanced theoretical approach based on a state-space representation using modal parameters.A case study of a real shaft train is shown, including a comparison of achieved results using the SDOF and the presented MDOF approach. By validating with experimental results, the excellent prediction quality of the MDOF approach is confirmed. The implementation of this approach enabled to further improve the reliability and the efficiency, which means high accuracy combined with low computation time, in performing rotordynamic assessments.Copyright

Residual Unbalance Determination for Flexible Rotors at Operational Speed

According to ISO 11342 the determination of residual unbalances of flexible rotors, e.g. turbine- and generator-rotors for power plants is based on a modal approach. It delivers good estimations for the residual modal unbalance close to critical speeds. However, the majority of flexible rotors are operated at speeds out of a resonance, where ISO 11342 does not provide a procedure or a criterion to estimate the balancing quality. This is in contradiction to customer demands, who often require a proof of the balancing quality particularly at this operating speed. In this paper a procedure is presented, how to estimate the residual unbalance for the operating speed as well.

Numerical Analysis of Influence Coefficients for On-Site Balancing of Flexible Rotors

Balancing of flexible rotors by means of Influence Coefficients is a well-known method in the theory of rotor dynamics. For a successful application of the method Influence Coefficients are needed. They are defined as the vibration response at one measurement point due to a single unbalance in one of the balancing planes. Influence Coefficients are usually determined by measurements in test runs with defined test weights. However, Influence Coefficients can also be determined by means of a numerical analysis. This needs of course a very good model for the rotor train, including all important rotor dynamic effects. In this project a trial is made to determine Influence Coefficients by means of modelling and numerical simulation.

A New Approach for Thermo-Elastic Equations to Predict Spiral Vibrations in Turbogenerator Shafts

The phenomenon of vibration vector rotation caused by thermally induced unbalance changes, referred to as the “spiral vibration” (SV), is frequently observed in large rotating machinery. Since the SV is a consequence of an interaction between mechanical and thermal unbalance of the rotor, a set of standard rotordynamic equations must be extended by the additional thermal equation. For the case of rotor deformation caused by a hot spot on a slip ring of turbo-generator a new thermo-elastic model has been formulated. A solution for the thermal mode response of a simplified system has been derived analytically using the non-dimensional form of the thermal equation. This paper provides formulae for stability threshold and spiral period corresponding to the newly developed model of thermal excitation. The presented theoretical results have been adopted in more detailed numerical models and used to effectively extend stability margin of the SV in turbo-generator shaft trains.

Rotordynamic Investigation of Spiral Vibrations: Thermal Mode Equation Development and Implementation to Combined-Cycle Power Train

Rotation of vibration vector caused by thermally induced unbalance changes is a frequently observed phenomenon in large rotating machinery. The heat arising from the friction losses, which are generated at the interfaces between rotating and statoric components of the machine, is partly absorbed by the shaft. This heat input is typically not uniform around the shaft circumference and the resulting temperature difference causes the rotor to bow. The excitation resulting from the sum of mechanical unbalance and thermal bow will lead to a slowly rotating (in the synchronously rotating coordinates system) whirl vector, whose magnitude can decrease or increase in time.A generic understanding of this effect (B.L. Newkirk in 1926, [4]) had been followed by a number of physical models representing specific heat exchange mechanisms (W. Kellenberger [3], J. Schmied [6], P. Morton [11]). A hot spot on the shaft surface can be generated at various locations of a shaft-line. Typical components responsible for thermally induced modulation of vibration vector are journal bearings, seal rings, labyrinth seals (in case of a soft rubbing). Furthermore carbon brushes sliding on the slip ring, supplying the DC current to the field winding of the generator rotor, were identified as a source of nonuniform heat input that may excite spiral vibrations (L. Eckert and J. Schmied in [7], [8]). These local heat input phenomena affect consequently the vibration behavior of the overall shaft train.This paper provides a new approach to the quantitative description of a heat exchange mechanism which leads to the hot spot generation on the surface of a slip ring. A new thermal equation has been formulated, which determines the stability and frequency of the thermal mode. Characteristics of spiral vibration are discussed based on the analytical solution of the Jeffcott rotor model coupled with the proposed thermo-elastic equation.The implementation of the described method to a full shaft-line model of a combined cycle, single shaft power train was done using the Finite Element Method. The results of this calculation were validated against measurement data. The paper shows how the applied computational approach can be used to extend stability margin of the spiral vibration in turbo-generator shaft trains.Copyright