International Journal of Machine Tools & Manufacture 44 (2004) 1151–1161 www.elsevier.com/locate/ijmactool Structural modeling of end mills for form error and stability analysis E.B. Kivanc, E. Budak  Faculty of Engineering and Natural Sciences, Sabanci University Orhanli Tuzla, 34956 Istanbul, Turkey Received 20 February 2004; received in revised form 25 March 2004; accepted 8 April 2004 Abstract Structural modeling of end mills is crucial for predicting deﬂections and vibrations in milling processes. End mill geometry is very complex which makes the use of simple beam models inaccurate. Stiﬀness and frequency response function (FRF) measure- ments need to be performed to identify the static and dynamic properties experimentally. This can be very time consuming considering the number of tool–tool holder combinations in a production facility. In this paper, methods for modeling structural properties of milling tools are presented. Static and dynamic analysis of tools with diﬀerent geometry and material are carried out by ﬁnite element analysis (FEA). Some practical equations are developed to predict the static and dynamic properties of tools. Receptance coupling and substructuring analyses are used to combine the dynamics of individual component dynamics. In this analysis, experimental or analytic FRFs for the individual components are used to predict the ﬁnal assembly’s dynamic response. Clamping parameters between the tool and the tool holder may eﬀect the results signiﬁcantly. These parameters are also identiﬁed from the measurements. The eﬀects of changes in tool parameters and clamping conditions are evaluated. The predictions are veriﬁed by the measurements for diﬀerent conditions. # 2004 Elsevier Ltd. All rights reserved. Keywords: Milling; Deﬂections; Stability 1. Introduction Tolerance integrity and surface quality of machine parts are of prime importance in milling processes as well as productivity. Static and dynamic deformations of machine tool, tool holder and cutting tool play an important role in tolerance integrity and stability in a machining process aﬀecting part quality and pro- ductivity. Excessive static deﬂection may cause toler- ance violations whereas chatter vibrations result in poor surface ﬁnish. Cutting force, surface ﬁnish and cutting stability models can be used to predict and overcome these problems. This would require static and dynamic characteristics of the structures involved in a machining system [1]. Considering great variety of machine tool conﬁgurations, tool holder and cutting tool geometries, analysis of every case can be quite time consuming and unpractical. These properties are usually obtained experimentally using stiﬀness mea- surements and modal analysis [1–3]. In this study, gen- eralized equations are presented which can be used for predicting the static and dynamic properties of milling system components. Due to its wide use in industry, milling process is considered, however, similar approa- ches can be applied to other machining operations as well. The structural models presented in this paper, together with the process models, can be used in the development of a virtual machining system where the physics of the process can be simulated in addition to the geometry and tool path in conventional CAD/ CAM applications. Modeling of milling process has been the subject of many studies some of which are summarized by Smith and Tlusty [4]. The focus of these studies has mostly been on the modeling of cutting geometry and force, stability and prediction of part quality [5–9]. The mech- anistic approach has been widely used for the force predictions and also has been extended to predict deﬂections and form errors [6–7]. An alternative method is to use mechanics of cutting approach in  Corresponding author. Tel.: +90-216-483-9519; fax: +90-216-483- 9550. E-mail address: ebudak@sabanciuniv.edu (E. Budak). 0890-6955/$ - see front matter # 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijmachtools.2004.04.002