Abstract—Cutting forces prediction is very important in micromilling for cutting tool’s design and process planning. This paper presents a new model for uncertainty estimation of dynamic cutting forces in micromilling using a type-2 fuzzy rule-based system. The type-2 fuzzy estimation not only filters the noise and estimates the instantaneous cutting force in micromilling using observations acquired by sensors during cutting experiments, but also assesses the uncertainties associated with the prediction caused by the manufacturing errors and signal processing. Moreover, the interval output of the type-2 fuzzy system gives very useful information to machine tool controllers in order to maximize material removal while controlling tool wear or tool failure to maintain part quality specifications. I. INTRODUCTION LONG with the increasing demand of miniaturization in electronics, medical, telecommunication, aerospace, automotive and defense industries, development of the micromilling process for micro-mould manufacturing is driven due to its capability of machining 3D free-form micro-structures from highly wear resistant materials that have to be heat treated before microcutting to achieve a reasonable surface finish [1]. However, the tool wears quickly in micromilling with the microscaled cutting tool (diameter < 1 mm) and the high speed (> 10,000 rpm). Reliable prediction of cutting forces in micromilling is essential for the design of cutting tools, as well as planning machining operations for maximum productivity and quality [2]. Due to the difficulty in understanding the exact physics of micromilling process, the information obtained during machining process is not yet complete and precise. The cutting forces are supposed to change periodically based on the tool load. It is hard to establish theoretical and analytical approach or mechanistic model by using this kind of information. A few investigations have been conducted for Manuscript received February 2, 2010. Q. Ren (corresponding author), Mechanical Engineering Department, École Polytechnique de Montréal, C. P. 6079, succ. Centre-Ville, Montréal, Québec, Canada, H3C 3A7 (phone: 514-340-4711 ex.3345; fax: 514-340-5867; e-mail: qun.ren@ polymtl.ca). L. Baron, Mechanical Engineering Department, École Polytechnique de Montréal, C. P. 6079, succ. Centre-Ville, Montréal, Québec, Canada, H3C 3A7 (e-mail: luc.baron@ polymtl.ca). K. Jemielniak , Faculty of Production Engineering, Warsaw University of Technology, Narbutta 86, 02-524 Warsaw, Poland (e-mail: k.jemielniak@wip.pw.edu.pl). M. Balazinski, Mechanical Engineering Department, École Polytechnique de Montréal, C. P. 6079, succ. Centre-Ville, Montréal, Québec, Canada, H3C 3A7 (e-mail: marek.balazinski@ polymtl.ca). predicting the micromilling forces with the precision needed. For example, analytical cutting force model [3], model based on the elastic contact between the tool and the workpiece [4], mechanistic model [5], Taylor-based model [6], ploughing force model [7], etc. The aim of this paper is presenting a new method for modelling dynamic cutting forces in micromilling using a type-2 fuzzy rule-based system. The type-2 fuzzy estimation not only filters and estimates the instantaneous cutting force in micromilling using observations acquired by sensors during cutting experiments, but also assesses the uncertainties associated with the prediction caused by the manufacturing errors and data processing. Moreover, the interval output of the type-2 fuzzy system gives very useful information to optimize the machining procedure. This paper has five sections. In Section I the importance of current cutting force modelling in micromilling and former researches are introduced. The theoretical foundation of fuzzy logic and type-2 TSK fuzzy rule-base system (FRBS) are recalled in Section II. The identification algorithm of type-2 fuzzy modelling based on subtractive clustering method is presented in Section III. A micromilling case study is in Section IV. The experimental results show the effectiveness and advantages of the type-2 TSK fuzzy modelling. Conclusions are given in Section V. II. TYPE-2 TSK FUZZY RULE-BASED SYSTEM A. TSK Fuzzy Logic Since fuzzy logic (FL) originally proposed by Zadeh in his famous paper “Fuzzy Sets” in 1965 [8], it is developing very fast and is widely used. FL provides a simple way to arrive at a definite conclusion based upon vague, ambiguous, imprecise, noisy, or missing input information. TSK fuzzy rule-based system (FRBS) [9, 10] was proposed in an effort to develop a systematic approach to generating fuzzy rules from a given input-output data set. This model consists of rules with fuzzy antecedents and mathematical function in the consequent part. The antecedents divide the input space into a set of fuzzy regions, while consequents describe behaviour of system in those regions. TSK fuzzy model is a very powerful tool for function approximation due to its capability to explain nonlinear relation using a relatively low number of simple rules. A generalized type-1 TSK model can be described by IF-THEN rules which represent input-output relations of a system. For a multi-input-single-output (MISO) first–order type-1 TSK model, its kth rule can be expressed as: Modelling of Dynamic Micromilling Cutting Forces Using Type-2 Fuzzy Rule-Based System Qun Ren, Luc Baron, member, IEEE, Krzysztof Jemielniak and Marek Balazinski A WCCI 2010 IEEE World Congress on Computational Intelligence July, 18-23, 2010 - CCIB, Barcelona, Spain FUZZ-IEEE 978-1-4244-8126-2/10/$26.00 c 2010 IEEE 2311