Towards obtaining robust boundary condition parameters to aid accuracy in FEA thermal error predictions

Finite Element Analysis (FEA) is used as a design tool within engineering industries due to the capability for rapid summative analysis accompanied by the visual aid. However, to represent realistic behaviour, FEA relies heavily on input parameters which must ideally be based on true figures such as data from experimental testing which sometimes requires time-consuming testing regimes. In the case of machine tool assemblies where complex structural joints and linkages are present, access to those areas can be a primary constraint to obtaining related boundary parameters such as heat flow across joints, for which, assumptions are incorporated to the FEA model which in effect increase the uncertainty in the FEA predictions. Similarly, in the case of thermal error modelling, simplifications are made when representing thermal boundary conditions such as the application of a uniform convection parameter to an assembly with parts assembled in both horizontal and vertical orientations. This research work aims to reduce the number of assumptions by providing experimentally obtained thermal boundary condition parameters. This work acknowledges experimental regimes that focus on obtaining thermal parameters related to the conduction across assembly joints (Thermal Contact Conductance-TCC) and measures the convection around areas such as belt drives and rotating parts to obtain convection parameters as inputs to the FEA. It provides TCC parameters for variable interfacial behaviour based on the varying contact pressure and the heat flow through dry and oiled contacts such as the conduction from spindle bearings to the surrounding housing and conduction from guideways into the associated assembly through carriages and contact bearings. It provides convection parameters across the test mandrel rotating at different speeds and around stationary structures such as convection parameters observed during TCC tests. It also provide details on the methods used to obtain all these parameters such as the use of thermal imaging, sensors placements and methods to obtain these boundary condition parameters. The significance of this work is to improve dramatically FEA thermal predictions, which are a critical part of engineering design. Although the focus is on machine tool design, the process and parameters can equally be applied to other areas of thermodynamic behaviour

Efficient estimation by FEA of machine tool distortion due to environmental temperature perturbations

Machine tools are susceptible to exogenous influences, which mainly derive from varying environmental conditions such as the day and night or seasonal transitions during which large temperature swings can occur. Thermal gradients cause heat to flow through the machine structure and results in non-linear structural deformation whether the machine is in operation or in a static mode. These environmentally stimulated deformations combine with the effects of any internally generated heat and can result in significant error increase if a machine tool is operated for long term regimes. In most engineering industries, environmental testing is often avoided due to the associated extensive machine downtime required to map empirically the thermal relationship and the associated cost to production. This paper presents a novel offline thermal error modelling methodology using finite element analysis (FEA) which significantly reduces the machine downtime required to establish the thermal response. It also describes the strategies required to calibrate the model using efficient on-machine measurement strategies. The technique is to create an FEA model of the machine followed by the application of the proposed methodology in which initial thermal states of the real machine and the simulated machine model are matched. An added benefit is that the method determines the minimum experimental testing time required on a machine; production management is then fully informed of the cost-to-production of establishing this important accuracy parameter. The most significant contribution of this work is presented in a typical case study; thermal model calibration is reduced from a fortnight to a few hours. The validation work has been carried out over a period of over a year to establish robustness to overall seasonal changes and the distinctly different daily changes at varying times of year. Samples of this data are presented that show that the FEA-based method correlated well with the experimental results resulting in the residual errors of less than 12 μm

FEA-based design study for optimising non-rigid error detection on machine tools

Non-rigid-body behaviour can have a considerable effect on the overall accuracy performance of machine tools. These errors originate from bending of the machine structure due to change in distribution of its own weight or from movement of the workpiece and fixture. These effects should be reduced by good mechanical design, but residual errors can still be problematic due to realistic material and cost limitations. One method of compensation is to measure the deformation directly with sensors embedded in a metrology frame. This paper presents an FEA-based design study which assesses finite stiffness effects in both the machine structure and its foundation to optimise the sensitivity of the frame to the resulting errors. The study results show how a reference artefact, optimised by the FEA study, can be used to detect the distortion

Application of multi sensor data fusion based on Principal Component Analysis and Artificial Neural Network for machine tool thermal monitoring

Due to the various heat sources on a machine tool, there exists a complex temperature distribution across its structure. This causes an inherent thermal hysteresis which is undesirable as it affects the systematic tool –to-workpiece positioning capability. To monitor this, two physical quantities (temperature and strain) are measured at multiple locations. This article is concerned with the use of Principal Component Analysis (PCA) and Artificial Neural Networks (ANN) to fuse this potentially large amount of data from multiple sources. PCA reduces the dimensionality of the data and thus reduces training time for the ANN which is being used for thermal modelling. This paper shows the effect of different levels of data compression and the application of rate of change of sensor values to reduce the effect of system hysteresis. This methodology has been successfully applied to the ram of a 5-axis gantry machine with 90 % correlation to the measured displacement

Thermal Error Modelling of a CNC Machine Tool Feed Drive System using FEA Method

Recirculating ball screw systems are commonly used in machine tools and are one of the major heat sources which cause considerable thermal drift in CNC machine tools. Finite Element Analysis (FEA) method has been used successfully in the past to model the thermal characteristics of machine tools with promising results. Since FEA predictions are highly dependent on the efficacy of numerical parameters including the surrounding Boundary Conditions (BC), this study emphasises on an efficient modelling method to obtain optimised numerical parameters for acquiring a qualitative response from the feed drive system model. This study was performed on a medium size Vertical Machining Centre (VMC) feed drive system in which two parameter dentification methods have been employed; the general prediction method based on formulae provided by OEMs, and the energy balance method. The parameters obtained from both methods were applied to the FEA model of the machine feed drive system and validated against experimental results. Correlation with which was increased from 70 % to 80 % using the energy balance method

Optimising temperature sensor placement for machine tool thermal error compensation

In this article, results of thermal error assessments are evaluated from a range of modern machine tools operating with active thermal compensation. The standard models assume a linear relationship between temperature and displacement and implementations address only a limited subset of error sources. However, significant residual errors were found on the analysed machines. The aim of this work is to improve the accuracy and increase the scope of compensated errors, without introducing onerous complexity, by using optimised linear correlation models applied to existing controllers

Extreme events and event size fluctuations in biased random walks on networks

Random walk on discrete lattice models is important to understand various types of transport processes. The extreme events, defined as exceedences of the flux of walkers above a prescribed threshold, have been studied recently in the context of complex networks. This was motivated by the occurrence of rare events such as traffic jams, floods, and power black-outs which take place on networks. In this work, we study extreme events in a generalized random walk model in which the walk is preferentially biased by the network topology. The walkers preferentially choose to hop toward the hubs or small degree nodes. In this setting, we show that extremely large fluctuations in event-sizes are possible on small degree nodes when the walkers are biased toward the hubs. In particular, we obtain the distribution of event-sizes on the network. Further, the probability for the occurrence of extreme events on any node in the network depends on its 'generalized strength', a measure of the ability of a node to attract walkers. The 'generalized strength' is a function of the degree of the node and that of its nearest neighbors. We obtain analytical and simulation results for the probability of occurrence of extreme events on the nodes of a network using a generalized random walk model. The result reveals that the nodes with a larger value of 'generalized strength', on average, display lower probability for the occurrence of extreme events compared to the nodes with lower values of 'generalized strength'