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Thermal errors are often quoted as being the largest contributor to inaccuracy of CNC machine tools, but they can be effectively reduced using error compensation. Success in obtaining a reliable and robust model depends heavily on the choice of system variables involved as well as the available input-output data pairs and the domain used for training purposes. In this paper, a new prediction model “Grey Neural Network model with Convolution Integral (GNNMCI(1, N))” is proposed, which makes full use of the similarities and complementarity between Grey system models and Artificial Neural Networks (ANNs) to overcome the disadvantage of applying a Grey model and an artificial neural network individually. A Particle Swarm Optimization (PSO) algorithm is also employed to optimize the Grey neural network. The proposed model is able to extract realistic governing laws of the system using only limited data pairs, in order to design the thermal compensation model, thereby reducing the complexity and duration of the testing regime. This makes the proposed method more practical, cost-effective and so more attractive to CNC machine tool manufacturers and especially end-users.
Conference Proceeding:
http://kth.diva-portal.org/smash/get/diva2:660817/FULLTEXT08.pdf

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All content in this area was uploaded by Ali M Abdulshahed on Feb 20, 2014

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... In contrast, other techniques use empirical modelling, where the model is based on the experimental measurements of the machine tool, rather than calibrating an existing model. Different model structures have been used to predict thermal errors in machine tools such as multiple regression analysis [4], types of artificial neural networks [5], fuzzy logic [6], an adaptive neuro-fuzzy inference system [7,8], Grey system theory [9] and a combination of several different modelling methods [10,11]. ...

... Also, similar works have been carried out by the same authors in Refs. [11,14,15]. ...

This paper presents a new modelling methodology for compensation of the thermal errors on a gantry-type 5-axis CNC machine tool. The method uses a “Grey Neural Network Model with Convolution Integral” (GNNMCI(1, N)), which makes full use of the similarities and complementarity between Grey system models and artificial neural networks (ANNs) to overcome the disadvantage of applying either model in isolation. A Particle Swarm Optimisation (PSO) algorithm is also employed to optimise the proposed Grey neural network. The size of the data pairs is crucial when the generation of data is a costly affair, since the machine downtime necessary to acquire the data is often considered prohibitive. Under such circumstances, optimisation of the number of data pairs used for training is of prime concern for calibrating a physical model or training a black-box model. A Grey Accumulated Generating Operation (AGO), which is a basis of the Grey system theory, is used to transform the original data to a monotonic series of data, which has less randomness than the original series of data. The choice of inputs to the thermal model is a non-trivial decision which is ultimately a compromise between the ability to obtain data that sufficiently correlates with the thermal distortion and the cost of implementation of the necessary feedback sensors. In this study, temperature measurement at key locations was supplemented by direct distortion measurement at accessible locations. This form of data fusion simplifies the modelling process, enhances the accuracy of the system and reduces the overall number of inputs to the model, since otherwise a much larger number of thermal sensors would be required to cover the entire structure. The Z-axis heating test, C-axis heating test, and the combined (helical) movement are considered in this work. The compensation values, calculated by the GNNMCI(1, N) model were sent to the controller for live error compensation. Test results show that a 85% reduction in thermal errors was achieved after compensation.

... Deformations due to the changes in the temperature of the machine tool structure create relative displacement between the tool tip and the workpiece during the machining process, which affects the dimensional accuracy of manufactured parts; these are known as the thermal errors [1], which have been reported to be approximately 70% of the total positioning error of the CNC machine tool [2]. Artificial Intelligence models have been shown to be efficient in thermal error modelling [3][4][5], since those methods are able to learn complex nonlinear relations and to treat imprecise data. However, these models are based on the input-output data patterns of the system under consideration. ...

... As a result of accumulation, one can potentially uncover a development tendency existing in the process of Grey accumulation so that the changing trend becomes more apparent and laws of integration hidden in the raw data can be sufficiently revealed [15]. Nowadays, it is combined with intelligent computational techniques such as neural networks [3, 16], genetic algorithm [17], and fuzzy logic [18]. These successful applications inspire us to explore Grey system characteristics to systematically address ANFIS modelling. ...

... For instance, Gebhardt et al. [39] formulated a grey box model to characterize the thermal behavior of a 5axis machine tool using the experimental data. Abdulshahed et al. [40] used grey system theory and neural networks on experimental data to predict the TCP distortion during an Environmental Temperature Variation Error (ETVE) test on a machine tool. Then robustness of the proposed model is validated with the experimental data not used during model training. ...

Thermal influences, on and by the machine tool are one of the main reasons for the machining error. Although both the internal and the external heat sources lead to the thermal error, their relative proportion is typically dependent on the operating conditions such as machining parameters, the duration of machining and availability of temperature-controlled space to name a few. Literature survey reveals that a significant portion of the research either addresses the effects of internal heat sources or a combination of internal and external heat sources since the de-facto standard is to commission the machine tool in a temperature-controlled space. However, in this work, only the influence of external heat sources, predominantly caused by ambient temperature variations onto the distortions observed at the Tool Center Point (TCP) is considered. Smart sensory device such as Resistance Temperature Detector (RTD) sensor data is used for the modelling of thermal distortion due to external heat sources. The model is inherently based on the development of a thermal network using a lumped system approach for the estimation of temperatures of machine tool components and then the TCP distortion using the construction relation. Further, the model is modified through the introduction of two aspects: first is the addition of thermal contact conductance as the machine tool components are practically connected; and the second is the parameterization of free convection heat coefficient from being a stationary value to a function of the ambient temperature. The proposed method is then applied to predict the thermal error on a vertical machining center subjected to environmental temperature variation. The results show that the model considering a combination of the thermal contact conductance and parameterized free convection coefficient leads to a closer agreement with the experimental data. The strategy along with a thermal compensation technique presented in this research successfully lead to the improved machining precision (approximately 70% of the original thermal error is addressed across the combinations) without a need of a conditioned environment for C-frame type vertical machining centers.

... Their validated results show significant average improvement by 41% of the errors on a free form. Abdulshahed et al. [20] applied an ANFIS with fuzzy c-means clustering to investigate the thermal deformation model. Different groups of key temperature points were identified from thermal images by using a novel schema based on a GM (0, N) method and fuzzy c-means clustering. ...

Thermal deformation is the main factor of the machining accuracy for grinding machines, which seriously restricts the precision improvement of grinding machines. However, at present, there are little researches on thermal error prediction, and the accuracy of the prediction model is comparatively low. Thus, a novel approach for thermal deformation prediction of grinding machine spindle based on heat energy conduction principle and neural network is proposed in this paper. Firstly, the temperature sensors’ pairs are applied to measure the temperature deviation between the spindle surface and its adjacent ambient which are directly related to the heat energy exchange. Secondly, the temperature deviations of each segment of the spindle are taken as inputs, which will exist and accumulate in the form of heat energy subsequently in the convolutional neural network. Meanwhile, the accumulated heat energy is mixed and transferred to the different segments of the spindle in the convolutional neural network. Thirdly, the thermal deformation caused by the increment of heat energy is considered as the output of thermal error prediction result based on the principle of heat energy conduction. Finally, the simulations and experiments are implemented to validate the feasibility and effectiveness of the proposed method.

... artificially intelligent approaches have also been applied to thermal error modeling in order to improve the accuracy and robustness of the error models. These artificial intelligence modeling techniques include artificial neural networks (ANNs) [18][19][20], fuzzy logic [19], adaptive neuro-fuzzy inference systems (ANFIS) [21] and integrations of the different modeling methods [22,23]. For example, Vanherck et al. ...

This paper is focused on developing a compensation module for reducing the thermal errors of a computer numerical control (CNC) milling machine. The thermal induced displacement variations of machine tools are a vital problem that causes positioning errors to be over than 65%. To achieve a high accuracy of machine tools, it is important to find the effective methods for reducing the thermal errors. To this end, this study first used 14 temperature sensors to examine the real temperature fields around the machine, from which four points with high sensitivity to temperature rise were selected as the major locations for creating the representative thermal model. With the model, the compensation system for controlling the displacement variation was developed. The proposed model has been applied to the milling machine. Current results show that the displacement variations on the x- and y-axes and the position error at the tool center were controlled within 20 μm when the compensation system was activated. The feasibility of the compensation system was successfully demonstrated in application on the milling operation.

... According to the results, the ANFIS with fuzzy c-means clustering produced better results, achieving up to 94 % improvement in error with a maximum residual error of ± 4 μm. In another work [8] they built a thermal model by integrating ANN and GMC(1, N) models. The thermal model can predict the Environmental Temperature Variation Error (ETVE) of a machine tool with reduction in error from over 20 μm to better than ± 3 μm. ...

Thermal errors can have a significant effect on CNC machine tool accuracy. The thermal error compensation system has become a cost-effective method of improving machine tool accuracy in recent years. In the presented paper, the Grey relational analysis (GRA) was employed to obtain the similarity degrees between fixed temperature sensors and the thermal response of the CNC machine tool structure. Subsequently, a new Grey model with convolution integral GMC(1, N) is used to design a thermal prediction model. To improve the accuracy of the proposed model, the generation coefficients of GMC(1, N) are calibrated using an adaptive Particle Swarm Optimisation (PSO) algorithm. The results demonstrate good agreement between the experimental and predicted thermal error. Finally, the capabilities and the limitations of the model for thermal error compensation have been discussed.

This paper presents an approach to compensate for the effect of thermal expansion on the structure of an industrial robot and thus to reduce the repeatability difference of the robot in cold and warm conditions. In contrast to previous research in this area that deals with absolute accuracy, this article is focused on determining achievable repeatability. To unify and to increase the robot repeatability, the measurements with highly accurate sensors were performed under different conditions on an industrial robot ABB IRB1200, which was equipped with thermal sensors, mounted on a pre-defined position around joints. The performed measurements allowed to implement a temperature-based prediction model of the end effector positioning error. Subsequent tests have shown that the implemented model used for the error compensation proved to be highly effective. Using the methodology presented in this article, the impact of drift can be reduced by up to 89.9%. A robot upgraded with a compensation principle described in this article does not have to be warmed up as it works with the same low repeatability error in the entire range of the achievable temperatures.

Analysis of the influence of the temperature on the positioning accuracy of the robot arm is one of the key problems in robotic assembly operations. The results of the analysis of the industrial robot positioning error presented in the article show that in conditions of stable temperature, these errors are systematic. Research on the influence of ambient temperature on the accuracy of the robot positioning was carried out for selected points in the working space of the robot arm. The Lillefors distribution was used to determine the influence of temperature on the distribution of the random variable. The results obtained were subjected to statistical analysis using the Shapiro-Wilk test. It was shown that to calculate the value of total error, the three-sigma rule may be used, because the flat normal distribution is concentrated around its expected value. Knowledge of the structure of the total error of the robot makes it possible to determine the location where the process can be carried out in which the robot has the least sensitivity to temperature-induced errors.

Recently, the convolution integral-based multivariable grey model (GMC(1, N)) has attracted considerable interest due to its significant performance in time series forecasting. However, this promising technique may occasionally confront ill-posed problem, which is a plague ignored by most researchers. In this paper, a regularized GMC(1, N) framework (R-GMC(1, N)) is proposed to estimate the grey coefficients in case there exists potential ill-posed problem. More specifically, we adopt two state-of-the-art regularization methods, i.e. the Tikhonov regularization (TR) and truncated singular value decomposition (TSVD), together with two regularization parameters detection methods, i.e. L-curve (LC) and generalized cross-validation (GCV), to identify the stable solutions. Numerical simulations on industrial indicators of China demonstrate that our methods yield more accurate forecast results than the existing GMC(1, N).

Thermal errors can have significant effects on CNC machine tool accuracy. The errors usually come from thermal deformations of the machine elements created by heat sources within the machine structure or from ambient change. The performance of a thermal error compensation system inherently depends on the accuracy and robustness of the thermal error model. In this paper, Adaptive Neuro Fuzzy Inference System (ANFIS), Artificial Neural Network (ANN) and Particle Swarm Optimization (PSO) techniques were employed to design four thermal prediction models: ANFIS by dividing the data space into rule patches (ANFIS-Scatter partition model); ANFIS by dividing the data space into rectangular sub-spaces (ANFIS-Grid partition model); ANN with a back-propagation algorithm (ANN-BP model) and ANN with a PSO algorithm (ANN-PSO model). Grey system theory was also used to obtain the influence ranking of the input sensors on the thermal drift of the machine structure. Four different models were designed, based on the higher-ranked sensors on thermal drift of the spindle. According to the results, the ANFIS models are superior in terms of the accuracy of their predictive ability; the results also show ANN-BP to have a relatively good level of accuracy. In all the models used in this study, the accuracy of the results produced by the ANFIS models was higher than that produced by the ANN models.
Full paper available at:
http://eprints.hud.ac.uk/17011/4/ABDULSHAHED_Lamdamap2013.pdf

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.

The scientific background that grey systems theory comes into being, the astonishing progress that grey systems theory has made in the world of learning and its wide-ranging applications in the entire spectrum of science, and the characteristics of unascertained systems include incomplete information and inaccuracies in data are presented in this paper. The scientific principle of simplicity and how precise models suffer from inaccuracies are also shown. We compared grey systems with other kinds of uncertainty models such as stochastic probability, rough set theory, and fuzzy mathematics. Finally, the elementary concepts and fundamental principles of grey systems, and main components of grey systems theory are introduced briefly.

A combined thermal and geometric error compensation system with a flexible structure that is general purpose in its application to any machine tool was described. The compensation system was found to be flexible, quick and simple to program. It was used to reduce thermal movements between the tool and the workpiece by over 6 times using a quick heating and cooling test for calibration. The error and warning messages were found to quickly identify modeling errors. The system has shown itself to be tolerant of sensor failures.

Thermal effect on machine tools is a well-recognized problem in an
environment of increasing demand for product quality. The performance of
a thermal error compensation system typically depends on the accuracy
and robustness of the thermal error model. This work presents a novel
thermal error model utilizing two mathematic schemes: the grey system
theory and the adaptive network-based fuzzy inference system (ANFIS).
First, the measured temperature and deformation results are analyzed via
the grey system theory to obtain the influence ranking of temperature
ascent on thermal drift of spindle. Then, using the highly ranked
temperature ascents as inputs for the ANFIS and training these data by
the hybrid learning rule, a thermal compensation model is constructed.
The grey system theory effectively reduces the number of temperature
sensors needed on a machine structure for prediction, and the ANFIS has
the advantages of good accuracy and robustness. For testing the
performance of proposed ANFIS model, a real-cutting operation test was
conducted. Comparison results demonstrate that the modeling schemes of
the ANFIS coupled with the grey system theory has good predictive
ability.

This paper presents a review of the latest research activities and gives an overview of the state of the art in understanding changes in machine tool performance due to changes in thermal conditions (thermal errors of machine tools). The topics are focused on metal cutting machine tools, especially on turning and milling machines as well as machining centres. The topics of the paper thermal issues in machine tools include measurement of temperatures and displacements, especially displacements at the tool centre point, computations of thermal errors of machine tools, and reduction of thermal errors. Computing the thermal errors of machine tools include both, temperature distribution and displacements. Shortly addressed is also to avoid thermal errors with temperature control, the influence of fluids and a short link to energy efficiency of machine tools. The paper presents the summary of research work in the past and current. Research challenges in order to achieve a thermal stable machine tool are discussed. The paper apprehend itself as an update and not a substitution of two published keynote papers of Bryan et al. [28] in 1990 and Weck et al. [199] in 1995.

Thermally induced errors were identified as a large error source during diamond turning of micrometer-size optical structures. We investigate the effects of spindle growth, application of cutting fluid mist, and temperature variation errors (TVEs), or thermal drifts, on the ability to hold tool position tolerances. It is shown how certain process variables, such as opening and closing of doors around the machine, affect the TVE. A first-order temperature model was derived to predict the TVE of the manufacturing process. The model uses the ambient temperature inside the machine enclosure because the part temperature could not be measured directly during machining. Documented long-term drift errors over 23 h were as large as 1.7 mu m. Short-term drift errors from pass to pass were as large as 0.3 mu m. Transient effects caused displacement shifts as large as 0.9 mu m. (C) 2007 Society of Photo-Optical Instrumentation Engineers.

The grey theory can be applied in the research of prediction, decision-making and control, especially in prediction. The primary characteristic of a grey system is the incompleteness of information. A grey system could be whitened by way of inserting more messages in itself and its accuracy of prediction could be raised. The solution to the existing grey prediction model GM(1,n) is inaccurate and then its prediction accuracy cannot be expected. To solve the existing GM(1,n) by assuming step by step the first order accumulated generating operation data of the associated series to be constants is incorrect. The existing model GM(1,n) is seriously wrong even for a system having a nonnegative associated series with constant entries. There are currently only a few wrong papers based on the existing GM(1,n) model to be published. Almost all the improved prediction models based on the existing GM(1,n) model are correct. For example, the improved models are correct by convolution integral or fitting their forcing terms by several elementary functions. The algorithm of GMC(1,n) is applied to explain why the existing GM(1,n) model is incorrect in this article.

The stability and stabilization of a grey system whose state matrix is triangular is studied. The displacement operator and established transfer developed by the author are the indispensable tool for the grey system.