Optimal sensor placement based on model order reduction
P. Benner (a), R. Herzog (b), N. Lang (b), I. Riedel (b), J. Saak (a)
(a) Max Planck Institute for Dynamics of Complex Technical Systems, Computational Methods in Systems and Control Theory, Magdeburg
(b) Research group Numerical Mathematics (Partial
Differential Equations), Chemnitz University of Technology
In this paper, we consider optimal sensor placement problems for thermo-elastic solid body models. More precisely, the temperature sensors are placed in a near-optimal way, so that their measurements allow an accurate prediction of the thermally induced displacement of the tool center point (TCP) of a machine tool under thermal loading. An efficient calculation is based on a low-dimensional approximation of the thermal field. Different model order reduction methods are compared with respect to the accuracy of the estimated TCP displacement and the optimized sensor locations.
Workpiece temperature measurement and stabilization prior to dimensional measurement
N. S. Mian, S. Fletcher, A. P. Longstaff
University of Huddersfield
In- or close-to-process dimensional measurement of workpieces allows rapid detection of production errors, which allows responsive corrections. The time required for the component to reach thermal stability before measurement is a more sensitive issue than for post-process coordinate metrology in a measurement laboratory. The traditional approach of waiting for a nominal, empirically selected duration with the component “soaking” in the environment results in considerable inefficiencies. Similarly, surface temperature measurement can have significant uncertainty due to sensor accuracy, deployment and the correlation to the core component temperature. This research analyses surface temperature methods and then utilizes finite element analysis to predict the timespans required by a component to stabilise using different boundary conditions in order to optimise the quality process.
Measurement of test pieces for thermal induced displacements on milling machines
H. Höfer, H. Wiemer
Institute of Machine Tools and Control Engineering,
Within Collaborative Research Centre (CRC) “Transregio 96”, a test piece was developed to demonstrate the effectiveness of correction and compensation solutions on milling machines. Therefore the test piece can map the thermal proportion of the displacements. In this paper the used measurement strategy and the measurement results on three different coordinate measuring machines (CMM) are evaluated. In doing so, various influences on the measurement result are considered. The objective is a sturdy measurement strategy to achieve comparable measurement results independently from the used coordinate measuring machine.
Model reduction for thermally induced deformation compensation of metrology frames
J. v. d. Boom
ASML Netherlands B.V., The Netherlands
When wafers are exposed the change of heat load will introduce thermo-mechanical drifts of the metrology frames in lithography systems. These deformations lead to a decrease in positioning accuracy of the system affecting key performance indicators such as focus and overlay. To deal with these drifts compensation techniques are considered. Interpretation and implementation of low-order controllers is more straightforward, therefore, they are favored over complex high-order controllers. Real-time implementation of these low-order strategies ask for an approach where the high-order model for the thermo-mechanical behavior is reduced before controller synthesis is performed. Several model reduction techniques are investigated to arrive at the best reduced-order system model. This model is evaluated on prediction performance and usability.
Local heat transfer measurement
A. Kuntze, S. Odenbach, W. Uffrecht
Institute of Fluid Mechanics, TU Dresden
This contribution presents a thermoelectric sensor with a measurement area of approximately 1.2 mm² to determine heat transfer coefficients (HTC) on stationary as well as moving metallic machine components surrounded by fluid flow. The sensor is based on the temperature rise or over temperature method which is applied locally.