In order to produce components in optical quality in ultra-precision cutting processes it is very important to have a highly balanced system. Achieving the best possible balancing state is a time consuming process. Therefore, the prediction of the influence of the balancing state on the surface quality of the component is desirable. On the other hand, such a model should enable us to predict a necessary balancing state for a desired surface quality and thus save time in the balancing process. In this paper we present a model of an ultra-precision cutting experimental platform that determines vibrations and displacements of the platform caused by unbalances and forces from the cutting process. The actual cutting parameters are described by a second model. Since they depend on the unbalance displacements, both models have to be coupled to an interaction model. To compute balancing weights from vibrational measurements, regularization techniques for the solution of inverse and ill-posed problems are employed and presented.