Thermally induced deviations are a major contributor to positioning errors in machine tools, significantly impacting machining precision. This paper presents a model-reduction-based temperature field reconstruction method for volumetric error compensation. The temperature field is interpolated between temperature probe locations using projection basis vectors obtained through model order reduction of finite element models. Thermal effects such as convection are modeled as external heat loads, allowing their influence to be incorporated without requiring exact heat transfer coefficients or fluid temperatures. The approach allows thermal errors to be evaluated at arbitrary positions in the machine’s kinematic range, facilitating volumetric error compensation and integration with numerical compensation strategies. Experimental validation shows a good agreement with measured displacements. Maximum deviations of 19 m were observed, while the maximum reconstruction error is 1.1 m. The method’s computational efficiency and real-time capability make it a scalable and robust solution for model-based thermal error compensation in modern manufacturing machinery.

Nonlinearities are present in many coupling components of mechanical and mechatronic systems, with the most common nonlinear coupling property being that of friction force. Transient simulation of systems with nonlinear friction can be a challenge in terms of solver robustness and calculation time. Moreover, many manufacturing processes lead to periodic forces and motions such as in milling, or repetitive pick-and-place serial production operations. In this paper, a method and application for nonlinear periodic response analysis (NPRA) of reduced-order mechatronic systems is presented, which leverages the fact that the majority of components in common mechatronic systems (e.g. machine tools) are linear. The dynamic behaviour of these components can thus be represented using a linear reduced order model (ROM). The analysis is implemented using the Harmonic Balance Method (HBM), which is then applied to the ROM of a simple, structurally compliant mechatronic system with a motion controller and profiled rail guideways. A practical case encountered in industrial settings is analysed, that being the testing of a system’s frequency response. Periodic responses to a harmonic velocity setpoint input oscillation are analysed in both time and frequency domains and comparisons then made between measurement and simulation. This comparison shows that many significant effects of nonlinear friction in ROMs of mechatronic systems can be modelled using the NPRA method and a simple friction model with a presliding regime. The combination of HBM with model order reduction (MOR) opens up a field of applications for the efficient and robust simulative analysis of periodic processes with nonlinear couplings in complicated mechatronic systems.

A new method for predicting thermal displacements and dynamic characteristics of a machine tool using a digital twin to compensate for accuracy has been developed. The compensation method is based on an accu-racy prediction method using model order reduction to reproduce the behavior of machine tools digitally according to their physical characteristics. Additionally, by coupling with the digital twin of dynamics, a com-prehensive digital machine tool is generated. Using this model, the compensation of machining accuracy for ambient temperature conditions was validated on the actual machine. As a result, the error in the machining space was successfully compensated. Additionally, the dynamic cutting force was accurately estimated. A new method of compensation for thermal displacement and volumetric accuracy was established, which can visualize the actual machine phenomena in more detail than the conventional compensation of mathematical models by regression, machine learning, and neural networks.& COPY; 2023 CIRP. Published by Elsevier Ltd. All rights reserved.

Der digitale Zwilling als Modell gewinnt sowohl für die Entwicklung neuer Maschinengenerationen als auch für Simulationen parallel zum Betrieb stark an Bedeutung. Zur Erstellung entsprechender Modelle sind moderne flexible Mehrkörpersimulationsprogramme besonders geeignet. Im Rahmen dieses Beitrags wird die Simulationsumgebung MORe präsentiert, die sich unter anderem durch ihre Benutzerfreundlichkeit und ihre Recheneffizienz auszeichnet. Zudem ist die Berücksichtigung von Effekten möglich, die bisher im industriellen Umfeld kaum betrachtet wurden, wie beispielsweise Dämpfung.   The digital twin is becoming increasingly important for the development of new machine generations and for process parallel simulations. Modern flexible multi-body simulation programs are particularly suitable for creating the relevant models. In this paper, the simulation environment MORe is presented, which is characterized by its user-friendliness and its computational efficiency. Furthermore, it is possible to study effects such as damping, which have hardly been considered in industrial environments so far.

Thermo-mechanical finite element (FE) models predict the thermal behavior of machine tools and the associated mechanical deviations. However, one disadvantage is their high computational expense, linked to the evaluation of the large systems of differential equations. Therefore, projection-based model order reduction (MOR) methods are required in order to create efficient surrogate models. This paper presents a parametric MOR method for weakly coupled thermo-mechanical FE models of machine tools and other similar mechatronic systems. This work proposes a reduction method, Krylov Modal Subspace (KMS), and a theoretical bound of the reduction error. The developed method addresses the parametric dependency of the convective boundary conditions using the concept of system bilinearization. The reduced-order model reproduces the thermal response of the original FE model in the frequency range of interest for any value of the parameters describing the convective boundary conditions. Additionally, this paper investigates the coupling between the reduced-order thermal system and the mechanical response. A numerical example shows that the reduced-order model captures the response of the original system in the frequency range of interest.

A framework of methods for efficient and accurate simulation of the dynamics of machine tools including control is presented. The major achievements are a model order reduction technique with pre-definable error bound and a method for modelling of moving interfaces on flexible bodies based on trigonometric interpolation of the desired force distribution. The software tool MORe (Model Order Reduction and more) that implements thesemethods is presented. Application examples on analyses of dynamic and static properties are presented and simulation results are compared with measurements. The very good validation results confirm the usability of the presented methods and software for real-world applications.

Friction is a nonlinear phenomenon being present between moving components. For the axis of a machine tool, frictional and control effects have a strong influence on the system’s dynamic behavior. Due to their nonlinearity, frictional effects are usually modeled using time consuming transient simulations. This paper presents an approach to efficiently linearize frictional effects for a given excitation based on the nonlinear behavior of the system. The linear friction models can be used together with linear models of the control for an efficient frequency domain analysis of the dynamic behavior, while preserving high accuracy.

Increasingly integrated systems and the use of innovative lightweight structures enabled an evolution of the machine tool industry to products with very high dynamic performance and precision. For the development of modern machine tools, simulation has continuously gained in importance. However, due to increasing pressure to reduce the time-to-market of new products, an efficient work-flow for the integration of simulation in the design process is crucial. In this contribution, a newly developed design process named Design to Specifications (DtS) is presented. DtS places the focus on productivity and accuracy specifications for a machine tool and enables the design of structures that precisely meet the specifications. In a first step, requirements on structural properties are regarded. The requirements on dynamic capabilities as jerk or acceleration limitations are derived from productivity specifications, using computer aided manufacturing tools, and reference workpieces of choice. From requirements on dynamics and accuracy specifications, the required position controller bandwidth is derived, from which a minimum critical system eigenfrequency is deduced that allows a design engineer to select machine parts and to estimate proper dimensions for critical components. After having designed a particular structure, a virtual prototype is created that allows a time-saving verification of the dynamic capabilities of a machine tool by means of calculations in frequency domain. The calculation of maximum contour errors by means of weighted frequency response functions of the dynamic tracking error is presented. In summary, DtS enables an efficient design or modification of machine tool structures using an effective application of control theory estimations and verification using virtual prototypes. (C) 2018 The Authors. Published by Elsevier Ltd.

Mechatronic structures deform under static and dynamic loads. These deformations lead to deviations at the tool center point (TCP), affecting the reachable accuracy and/or productivity of the machines. The scope of this work is the comparison of calculations and measurements of different static and dynamic errors on a dynamic test bench. A reduced-order modelling approach is applied for the test bench modelling. It uses a combination of modal condensation and moment-matching methods with Krylov subspaces. The different modelling steps and requirements are presented. The same model is used for all static and dynamic evaluations presented within this paper. Static deformations, leading to roll and pitch deviations at the TCP of the test bench structure, are simulated using the described modelling methodology and validated by inclination measurements. The modal behavior of the system is investigated by calculation and compared to the measurements at a single axes position. The spatial change of the frequency response functions of the modelled system is investigated further, by calculation and measurement of the velocity open-loop FRFs of one axis for different machine configurations. In addition, a transient trajectory simulation is performed and compared to the Heidenhain KGM and encoder measurements. The large variety of comparisons shows the efficient applicability of the modelling environment MORe.

Accurate finite element machine modelling is typically connected with high computational costs. For this reason, machine structures are usually simplified or analysed only partially. In this paper, an efficient machine modelling technique is presented. It makes use of modal condensation and Krylov subspace model order reduction techniques for Finite-Element-models and Fourier element coupling for moving interfaces. The resulting model is stated to be accurate statically and below a definable frequency. Especially the benefit of having an accurate low order static and dynamic machine model for grinding machine and process simulation is outlined. This enables a full size transient simulation without simplification or omission of potentially important machine components. The modelling methodology is applied to a large and complex test rig for high performance dry grinding. This test rig is used to emulate the railway grinding process, where low frequency deviations are acoustically most relevant. In order to be later used for transient grinding simulations, all test rig components are modelled and assembled. For the validation of the model, its modes and mode-shapes are compared to the results of an experimental modal analysis performed on the real test rig. TCP frequency response functions are further compared between measurement and simulation. The potential use of the model for surface roughness and waviness simulations is shortly implied.

This paper presents an effective method for the synchronisation of multiple feed axes with differing controller bandwidths by delaying the set point trajectories of those axes with higher bandwidths. First, a simplified model of a cascade-controlled feed axis is defined, which allows the problem to be treated analytically. The problem of synchronisation of the feed axes is then analysed mathematically, leading to the hypothesis of synchronisation through a delay of the set points of the more dynamic axes. Subsequently, the dynamic error behaviour and boundaries of a feed axis are calculated. The optimal damping factor for a feed axis is shown to be 1/√2 and the dynamic error can be formulated in terms of the bandwidth and acceleration or jerk limit. The proposed method is proven through a simulation and verified based on experimental results. In addition, the stated error bounds are verified, and the limits of the applicability are determined.

Thermal errors of manufacturing machines induced by fluctuating environmental temperatures are one of the largest error sources in precision manufacturing. With the increased demand in high precision workpieces less thermal sensitive manufacturing machines are a requirement. In this paper a new simulative evaluation procedure of thermal tool centre point errors in frequency domain and its validation via measurements is presented. The approach allows evaluation of the thermal behaviour and the thermal errors influencing the positioning error of the machine. It is presented, that selective insulation of machine structure can reduce the amplitude of thermal errors at the thermal resonance frequency. (C) 2015 CIRP.