Modellbasierte Berechnung der Systemeigenschaften von Maschinenstrukturen auf der Steuerung

Abstract

Heutige Entwicklungen in der Maschinentechnik zielen mit zunehmenden Maß darauf ab auch Leichtbautechniken einzusetzen. Dies stellt aber die Maschinenentwickler häufig vor die Problemstellung der verringerten Steifigkeit und Dämpfung der Maschinen durch Verringerung der Masse. Aus Sicht der Steuerungstechnik existieren unterschiedliche Möglichkeiten auftretende Schwingungen der nachgiebigen Maschinenstrukturen zu vermeiden. Einige Schwingungsvermeidungsalgorithmen sind in gängigen industriell eingesetzten NC-Steuerungen integriert. Allerdings benötigen, die Methoden zur Parametrierung die aktuellen Resonanzfrequenzen der Maschine, die je nach Position und Orientierung der Maschinenachsen unterschiedlich ausfallen. Resonanzfrequenzen von Maschinenstrukturen können über die experimentelle modale Analyse oder durch Simulationsmodelle vorab bestimmt werden und der Steuerung als Tabellen zur Verfügung gestellt werden. Die realen, momentanen Resonanzfrequenzen können bei Anregung alternativ auch mit Sensoren, welche in die Maschine integriert sind, ermittelt und berechnet werden. Demgegenüber steht die Performance der Steuerungshardware, die heutzutage hoch genug ist um Resonanzfrequenzen aus Simulationsmodellen auch online auf der Steuerung zu identifizieren. Der Vorteil dieser Methode liegt vor allem darin, dass teure Sensorik und aufwändige Messvorgänge vermieden werden. In der Arbeit wird aus diesen Gründe eine Methodik untersucht, die eine Online-Identifikation von Resonanzfrequenzen anhand von Simulationsmodellen erlaubt. Diese Methode soll neue Möglichkeiten bieten, um bestehende Schwingungsvermeidungsalgorithmen mit Informationen zu versorgen, wodurch eine Verbesserung der Genauigkeit der Maschinen angestrebt wird. Der Fokus der Arbeit liegt dabei auf der schnellen Berechnung von Maschineneigenschaften, welche auf Genauigkeit und Effizienz hin untersucht werden und für die Schwingungsvermeidung verwendet werden.

By reducing mass in machine components it is possible to minimize the energy consumption during the movement of the machine. Unfortunately this leads often to a higher compliance with less damping in the machine components. With standard dynamics in positioning a higher tendency to vibrations of the machine can be expected. Advanced open- and closed loop control concepts are technically capable of providing good disturbance rejection for low damped machines mechatronically, but they have often been rejected by the manufacturing industry because of the strong theoretical background and expert knowledge which is required for their application to practical problems. For the usage of the techniques the knowledge of the machine properties, i.e. eigenfrequency and damping, is necessary. There are different vibration avoidance techniques which require even the knowledge of the instantaneous machine properties or the upcoming machine properties as scheduling input to the controller. To minimize the effort for acquiring information about those properties through measurement and storing the resulting large amounts of data on a machine control, simulation models can be used to identify the behaviour. Nowadays, simulation models are typically created during the design of a machine. Those models, which are usually FE-models, can be used to support the vibration suppression techniques. Helpful seems the deployment in the PC-based control technique. Todays control devices typically use just a small amount of their computing power to control the machine. Therefore, the idea arises to use the standard PC-based control device and integrate a simulation environment. On this environment simulation models from the engineering process can be used to identify the instantaneous machine behaviour depending on the pose of the machine. The present work deals with the integration of standard FE-models into a newly developed simulation environment on the control device. Here techniques have been developed to feed vibration suppression techniques with information about the instantaneous and upcoming machine behaviour calculated by the model. Especially in production machines long distance travel of axes have a high impact on the machine behaviour. To represent this long distance travel of axes in the flexible multi-body simulation componentwise modelling of FE-models can be used and coupled depending on the actual pose of the machine. The coupling of those components is done between the input/output nodes of the single components. To have an accurate representation of the model, typically a high number of nodes are necessary. A mathematical technique for coupling the components has been established in the work for a state space model, which integrates all coupling information into the system matrix. The technique is based on the so called penalty technique, where spring and dampers are used as coupling elements. The coupling is done in a short cycle time to always achieve a most accurate pose dependent complete model. For a fast identification of the complete model small matrices allow a faster calculation. Therefore, reduction techniques need to be investigated and evaluated, which are suitable for the identification. Here, several techniques have been analyzed and the modal reduction has been detected to be the technique with the highest possible reduction and is mature enough to be used in industry. The good reduction capability results from the fact that the size of the resulting system matrix is not dependent on the number of input/output nodes. Another important benefit of the modal reduction technique appears in the resulting matrix in state space form, which is sparse and diagonally occupied. The evaluation of the technique has been done on an academic example with a mass, which travels along a simple beam. Here, comparisons have been made between a coupled model in a FE-tool and the coupling between two reduced FE-models in a CACE-tool. To identify the actual system behaviour, i.e. eigenfrequencies and the damping rates, the complete model needs to undergo an eigenvalue calculation within short cycles. Therefore, the investigations of the work are focused on finding an eigenvalue method, which calculates eigenvalues efficiently for small to middle sized matrices. The most suitable method – the so called QR-algorithm with double shift – has been identified. For this method a fast calculation of eigenvalues could be shown under real-time conditions. The method itself is not real-time capable, because it is iteratively calculating the eigenvalues. Since eigenvalues do not change rapidly within the short cycle times, they can be used as starting values for the next cycle step. It could be shown, that by indicating the previously calculated eigenvalues a faster calculation of a single eigenvalue is possible instead of calculating all eigenvalues. The results show that a calculation of single eigenvalues as well as all eigenvalues of a reduced system is possible in a cycle time of milliseconds on a standard PC. Tests have been made on an academic example under real-time conditions. All the algorithms need to run on the control device on a simulation environment. Thus, an already existing simulation environment i.e. the virtuos solver of the company ISG has been modified to run as a real-time task on the control device. Data exchange with the CNC and the PLC can be made as well in real-time. For safety reasons a special watchdog clamp is integrated into the control architecture into the safety circuit, to avoid damage of the machine or harm of users, in case of simulation- or model calculation errors. The user interface of the simulation environment has been upgraded to import modally reduced FE-models from a FE-tool and easily combine different models depending on their aggregation. The combination is arranged in a block structure typically found in CACE-tools. By the simple usage it is made sure that it will be adopted by industry. To test the method together with the vibration suppression techniques a test rack has been developed and assembled, which consists of two linear axes and a mass, which represents a processing head. The machine has been modelled componentwise as FE-models and integrated into the control device following the method, which has been developed. The results under real-time conditions show, that a fast calculation of the system behaviour is possible in a time scale of milliseconds and therefore is useful for the foreseen vibration suppression techniques. Finally, vibration suppression has been used to show the benefits of the method. Here the simple method of jerk limitation has been employed, which is already integrated in the CNC. The jerk limits have been set by the data which is gained from the model. By this the vibrations of the machine could be highly suppressed especially under dynamic movements.