Balancing of rotating machines based on the Kriging surrogate approach

One of the most applied procedures in the industry is the balancing of rotors, which can be achieved in different ways. Among the various techniques already studied, the signal-based ones are the most used, such as the four rounds without phase, modal balancing, and the influence coefficients method. However, these techniques present some drawbacks such as being time-consuming, and requirement of intrinsic linear behavior, which avoids the application of the previously mentioned techniques to nonlinear rotor systems. Additionally, trial weights are required to determine the relationship between vibration responses and unbalance forces. In the present contribution, a Kriging surrogate-based balancing approach is proposed. The proposed balancing approach uses the vibration responses and the correction masses (together with their corresponding angular positions) given by the influence coefficients (IC) method as samples for the Kriging surrogate model. Once the samples are defined and ready to be used, the Kriging surrogate model is determined. For new unbalance scenarios it is possible to predict the corresponding correction masses and their corresponding angular positions without using the so-called trial weights. In this case, the surrogate is formulated by considering the rotor unbalanced vibration amplitudes and their corresponding phase angles as inputs, and the associated correction masses and their corresponding angular positions as outputs. The obtained results demonstrate the effectiveness of the proposed technique for one-plane balancing procedures. Furthermore, it is possible to observe that trial weights are no longer required after a few balancing applications.