Principle and Verification of a Structure Model Based Correction Approach

Thiem, Xaver; Riedel, Mirko; Kauschinger, Bernd; Müller, Jens

doi:10.1016/j.procir.2016.03.169

Cited by 4 publications

(4 citation statements)

References 9 publications

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“…This would eventually allow to use full FEM models as part of filter-based approaches that combine model and measurements into best estimates of the state of a machine [30]. Furthermore, coupling a FEM model with a suitable model for error compensation and validating it in a realistic experimental setting [31] would be an important next step.…”

Section: Discussionmentioning

confidence: 99%

Toward transient finite element simulation of thermal deformation of machine tools in real-time

2018

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Finite element models without simplifying assumptions can accurately describe the spatial and temporal distribution of heat in machine tools as well as the resulting deformation. In principle, this allows to correct for displacements of the Tool Centre Point and enables high precision manufacturing. However, the computational cost of FEM models and restriction to generic algorithms in commercial tools like ANSYS prevents their operational use since simulations have to run faster than real-time. For the case where heat diffusion is slow compared to machine movement, we introduce a tailored implicit-explicit multi-rate time stepping method of higher order based on spectral deferred corrections. Using the open-source FEM library DUNE, we show that fully coupled simulations of the temperature field are possible in real-time for a machine consisting of a stock sliding up and down on rails attached to a stand. 15 though accurate specification of boundary conditions can be a challenge [4]. Accurate transient finite element models are very useful as they can provide spatially and temporally resolved temperature fields for machines with complex designs and geometries [3,5]. In contrast to empirical approaches [6, 7], the parameters in FEM are physical quantities that can, at least theoretically, be 20 measured. Since reduced models are typically machine-specific, their derivation also comes with a high cost in terms of person hours. In contrast, the mesh for FEM models can be generated automatically, e.g. from CAD files, even for machines with complex geometries.The disadvantage of FEM models is their high computational cost, which 25 is why often reduced models are employed, sacrificing accuracy or generality for speed. Running full time-dependent FEM models is considered too computationally expensive to be possible in real-time: "application of the original FE-models without any simplifications [...] for model-based control-integrated correction is very time-consuming and thus impractical" [8]. Despite only re-30 solving one machine part and employing a time-averaged heat source instead of a full coupling, Galant et al. report a computation time of around 5 hours to simulate a milling machine with 16,626 degrees-of-freedom over 16 hours using ANSYS (corresponding to η = 3.2). To the best of the authors' knowledge, there are no reports of simulations solving in real-time the fully coupled tran-35 sient FEM problem for a machine with moving parts without simplifications.Recent review papers also make no mention of such efforts [1,3,9]. A combination of finite differences and FEM, called FDEM, has been proposed that reduces computational effort but still relies on the use of macro elements to reduce the size of the solved system [2]. With respect to FDM and FEM, in a 40 review from 2017, Cao et al. state that "[...], due to the low efficiency, the computational models were rarely used in online thermal error compensation" [10], mentioning only approaches that rely on steady-state FEM models [11,12].A key reason is probably...

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Section: Discussionmentioning

confidence: 99%

Toward transient finite element simulation of thermal deformation of machine tools in real-time

2018

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“…Another possibility for a direct image-based pose calculation is photogrammetry, where a 3D object is reconstructed from a set of images taken from different points of views; see, for example, [38,39]. Disadvantages of this concept for high-precision pose measurements are the huge amount of data that is required for obtaining a complete 3D model of the scanned object and the complex and time-consuming computation.…”

Section: Direct Image-based Pose Calculationmentioning

confidence: 99%

High-Precision Absolute Pose Sensing for Parallel Mechanisms

Schempp

Schulz

2022

Sensors

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A parallel mechanism’s pose is usually obtained indirectly from the active joints’ coordinates by solving the direct kinematics problem. Its accuracy mainly depends on the accuracy of the measured active joints’ coordinates, the tolerances in the active and passive joints, possible backlash, axes misalignment, limb deformations due to stress or temperature, the initial pose estimate that is used for the numerical method, and the accuracy of the kinematic model itself. Backlash and temperature deformations in the active joints especially hinder high-precision applications as they usually cannot be observed. By implementing a camera module on the base platform and an array of fiducial tags on the moveable manipulator platform of a parallel mechanism, a highly accurate, direct, and absolute pose measurement system can be obtained that can overcome those limitations. In this paper, such a measurement system is proposed, designed, and its accuracy is investigated on a state-of-the-art H-811.I2 6-axis miniature hexapod by Physik Instrumente (PI) GmbH & Co. KG.

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“…Furthermore, define a number m < N and a weighting function (1) which maps an m-sized subset S to a real number greater or equal zero. Consequently, the "Optimal Subset Problem" becomes the minimization of this weighting function  as (2) In our application, the weighting function  is a function calculating the interpolation error which occurs when the m node values of S are used to build the radial basis interpolation function fS like in Glänzel et al [11], evaluate it in all N nodes of the set V and compare the interpolated values with the given values wi. Possible error measures are the sum of squares (3) or a pointwise computed maximum error (4) Clearly the value of  (S) is (aside from small rounding errors) zero if m = N, that is S = V, but it becomes greater than zero for m < N.…”

Section: Clustering Of Heat Transfer Coefficients By Optimal Subset Pmentioning

confidence: 99%

“…This is more complicated by the fact that CFD simulations work with finite element (FE) discretizations of the surrounding air which need to be changed when the machine tool axis positions or the direction of the air flow changes. This presents a massive additional computational effort which is especially problematic for simulation based online TCP correction methods, such as the structure model based correction, see Kauschinger et al [2].…”

Section: Introductionmentioning

confidence: 99%

Efficient Quantification of Free and Forced Convection via the Decoupling of Thermo-Mechanical and Thermo-Fluidic Simulations of Machine Tools

Glaenzel

Ihlenfeldt

Naumann

et al. 2018

Journal of Machine Engineering

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Thermo-elastic deformations represent one of the main reasons for positioning errors in machine tools. Investigations of the thermo-mechanical behaviour of machine tools, especially during the design phase, rely mainly on thermo-elastic simulations. These require the knowledge of heat sources and sinks and assumptions on the heat dissipation via convection, conduction and radiation. Forced convection such as that caused by moving assemblies has both a large influence on the heat dissipation to the surrounding air. The most accurate way of taking convection into account is via computational fluid dynamics (CFD) simulations. These simulations compute heat transfer coefficients for every finite element on the machine tool surface, which can then be used as boundary conditions for accurate thermo-mechanical simulations. Transient thermo-mechanical simulations with moving assemblies thus require a CFD simulation during each time step, which is very time-consuming. This paper presents an alternative by using characteristic diagrams to interpolate the CFD simulations. The new method uses precomputed thermal coefficients of a small number of load cases as support points to estimate the convection of all relevant load cases (i.e. ambient conditions). It will be explained and demonstrated on a machine tool column.

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Principle and Verification of a Structure Model Based Correction Approach

Cited by 4 publications

References 9 publications

Toward transient finite element simulation of thermal deformation of machine tools in real-time

Toward transient finite element simulation of thermal deformation of machine tools in real-time

High-Precision Absolute Pose Sensing for Parallel Mechanisms

Efficient Quantification of Free and Forced Convection via the Decoupling of Thermo-Mechanical and Thermo-Fluidic Simulations of Machine Tools

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