A Model-Based Prediction of Balancing Behavior of Rotors Above the Speed Range in Available Balancing Systems

Rotor balancing is probably the most discussed topic in the entire literature about rotor dynamics. In fact, it can also be said that the rotor dynamics itself arises from the problem of rotor balancing. Dating back to the 19th century, Rankine's studies stated that it was impossible to reach a high rotational speed, those of Dunkerley, in which the concept of critical speed was introduced, and the subsequent model of rotor with rigid disc in the middle (which, depending on the preferences, it is attributed to Jeffcott, De Laval or Föppl), developed in the 19th and 20th centuries, are based on the effects caused by rotor unbalance.

It would therefore seem that, from the point of view of theory, this is a problem of little interest, although in the literature scholars continue to publish papers that present methods to balance rotors, even of complex geometry, reducing the number of trials. However, balancing is very relevant in the industrial practice and sometimes there are very particular cases that cannot be addressed and solved by traditional methods.

The case described in this paper is just one of these and presents what could be defined as "predicting the effect of balancing" at rotational speeds that are higher than those possible on balancing machines.

It is customary for industrial steam turbine rotors to be balanced at low speed and then at high speed on balancing machines confined to special bunkers for safety reasons and equipped with specific bearings and supports. The standard balancing procedure requests to reach higher speed than the normal operating speeds at the site up to a defined trip speed TS. Furthermore an overspeed test is required to guarantee the assessment of the blades on the rotor.

When the rotor of the case considered has been balanced in the bunker, the bearing and the supporting structure are not those of the entire unit in the plant. Namely, the bearings are plain elliptical journal bearings and the supports are those suitable for the rotor on the balancing machine installed in the bunker. This implies that the dynamic characteristics of the unit, first of all the critical speeds, are different in the bunker and in the plant. Considering that both bearing and support stiffnesses are less than those of the plant, a trivial rule of thumb in rotor dynamics allows forecasting that critical speeds are lower in the bunker than in the plant.

Moreover, rotordynamic analysis shows that the second critical speed in the bunker, for the considered rotor, is very close to the TS in the plant. Not only industrial procedures, but also good rotordynamics practices, suggest reducing the speed test during the balancing and not to reach the TS.

However, rotordynamics modeling, identification techniques developed by the authors and the available vibration measurements allow the simulation of the behavior, i.e. the vibrations, of the entire unit in the bunker even at rotational speeds higher than those are possible to be reached, also up to the actual value of the TS.

Therefore, the following steps has been performed in order to simulate the behavior of rotor up to the actual TS in the bunker.

Set-up of the rotodynamic model of the considered turbine. This last requires the assembling of 3 sub-models:

Rotor model;

Bearing models;

Pedestal models.

Conversion of the raw data measured on the balancing machine in the bunker to rotor displacements in the measuring planes.

Identification of the equivalent residual excitations on the turbine, by means of a model based identification technique in the frequency domain.

Simulation of the vibrations of turbine, by using the rotordynamic model and the equivalent residual excitations.

Rotordynamics calculations, identification of the equivalent residual excitations and simulation of the vibrations are performed by using computer codes developed by the Dept. of Mechanical Engineering of Politecnico di Milano. These codes have been validated by means of several experimental tests.