Methods for high precision balancing of machine tools

The goal of the research project is the development of a general model for the description of the attainable construction unit quality (topography, shape accuracy etc.) as function of the imbalance state and the structure configuration by the example of ultra precision machining. In order to manufacture components in optical quality, highly exact machines and diamond tools are necessary. Imbalance driven oscillations can lead to a significant decrease of the surface quality. In particular surface roughness and shape accuracy will be affected by these oscillations. At present the best possible balancing is realized and afterwards the reached construction unit quality is examined. However, to achieve a given surface quality, it might not be necessary to do a time consuming best balancing of the system. Thus there exists a substantial economic potential if a prognosis of the attainable workpiece quality were possible during the process by an interpretation of the system state as well as its description by a set of integrated parameters. The computation of balancing weights can also make the process much more efficient. The connection of an imbalance distribution and the resulting oscillations of a rotating system can mathematically be described by a (possibly nonlinear) differential equation. The reconstruction of an imbalance distribution or the determination of balancing weights from vibrational measurements is an inverse and ill - posed problem. In this project we would like to develop methods that allow the determination of imbalance distributions from noisy vibrational measurements based on a model of the machine tool under consideration. With given balancing plains, we will determine the best positions and weights for the balancing process. Additionally, we would like to investigate the connection of the remaining vibrations and the achieved surface quality. This research project is planned in co-operation with the Laboratory for Precision Machining (LFM) at the University of Bremen (Professor Brinksmeier, separate proposal). Based on an experimental platform, the LFM will supply the data necessary for the system analysis. The prognoses computed at RICAM and ZeTeM should be experimentally verified at LFM.

The manufacturing of components in optical quality, e.g., astronomical mirrors, requires ultra precise machine tools. Depending on the intended form of the surface, which might be plane, spherical or aspherical, the workpieces have to be mounted on-axis or off-axis onto the spindle. This usually leads to significant imbalances in the system. Due to the resulting vibrations, the surface quality significantly reduced unless the system is well balanced. At present, a time consuming balancing process is applied in order to achieve the best possible balancing, even if such a good balancing state is not needed in order to achieve the desired surface quality. This research project aims at the development of a general model for the description of the attainable construction unit quality (topography, shape accuracy etc.) as a function of the imbalance state and the structure configuration, which is investigated for the example of ultra precision machining. The goal is not only to be able to compute the achievable surface quality for a given imbalance state, but also the determination of a imbalance state necessary for the realization of a prescribed surface quality. Thus, a costly fine - tuning of the imbalance state can be avoided. The project was carried out in close cooperation with the Laboratory for Precision Machining (LFM) and the Centre for Industrial Mathematics (ZeTeM) of the University of Bremen. The project is originally scheduled for 4 years, subdivided in 2 years sections. Within the first section, a structural model of an experimental platform of a cutting machine, installed and operated at the LFM, was created. It allows the computation of machine vibrations for given loads from imbalances and forces from the cutting process. At the same time a model describing forces and displacements from the cutting process was developed at ZeTeM. Both aspects are connected, and therefore a coupling of both models is necessary. The displacement of the diamond tool now also includes influences from the imbalance state, and therefore the resulting surface of the workpiece can be obtained. The modelling of the surface from the displacements of the diamond tool was done by ZeTeM. In summary, the resulting full model allows the prediction of the surface quality for a given imbalance distribution in the machine. Additionally, the structural vibration model enables us to determine an unknown imbalance distribution and resulting balancing masses from vibration measurements at the rotating machine.