Receptance coupling for tool point dynamic prediction by fixed boundaries approach Iker Mancisidor a,n , Aitor Urkiola a , Rafael Barcena b , Jokin Munoa a , Zoltan Dombovari c , Mikel Zatarain d a Dynamics and Control, IK4-Ideko, Arriaga Industrialdea 2, 20870 Elgoibar, Basque Country, Spain b Department of Electronic Technology, University of Basque Country (UPV/EHU), School of Industrial Technical Engineering, 3 Rafael Moreno Ave., 48013 Bilbao, Basque Country, Spain c Department of Applied Mechanics, Budapest University of Technology and Economics, Muegyetem rkp. 3, H-1111 Budapest, Hungary d Head of Scientific Development, IK4-Ideko, Arriaga Industrialdea 2, 20870 Elgoibar, Basque Country, Spain article info Article history: Received 5 September 2013 Received in revised form 12 December 2013 Accepted 23 December 2013 Available online 8 January 2014 Keywords: Chatter Milling Receptance coupling abstract The material removal capability of machines is partially conditioned by self-excited vibrations, also known as chatter. In order to predict chatter free machining conditions, dynamic transfer function at the tool tip is required. In many applications, such as high-speed machining (HSM), the problematic modes are related to the flexibility of the tool, and experimental calculation of the Frequency Response Function (FRF) should be obtained considering every combination of tool, toolholder and machine. Therefore, it is a time consuming process which disturbs the production. The bibliography proposes the Receptance Coupling Substructure Analysis (RCSA) to reduce the amount of experimental tests. In this paper, a new approach based on the calculation of the fixed boundary dynamic behavior of the tool is proposed. Hence, the number of theoretical modes that have to be considered is low, instead of the high number of modes required for the models presented up today. This way, the Timoshenko beam theory can be used to obtain a fast prediction. The accuracy of this new method has been verified experimentally for different tools, toolholders and machines. & 2014 Elsevier Ltd. All rights reserved. 1. Introduction In recent years, high-speed machining has been widely applied in aerospace industry, due to the good machinability provided by aluminum alloys. In this type of application, typically, up to 95% of the initial material can be removed. Under these conditions, the main limitation in the material removal rate is self-excited vibrations, also known as chatter, because they cause a reduction in the surface quality and in the lifetime of mechanical elements and tools. One of the most popular techniques to avoid chatter is the employment of stability diagrams in order to determine the best cutting conditions. These so-called stability lobes separate the stable and unstable regions depending on the spindle speed and depths of cut. Right now, the main reference among stability models is the zero order approach, proposed by Altintas and Budak [1]. This semi-analytical model has been shown to be very precise, but in case of special tool geometries and low immersion milling, the existence of additional stability lobes related to flip bifurcations and mode interactions were found [2]. These inaccuracies can be solved by the employment of other models, both in frequency domain [3] and in time domain [4]. The common point of stability models is the fact that they all require accurate measurements of FRF at the tool tip. The problem is that the measurements have to be repeated for each combina- tion of tool/toolholder/spindle. In order to overcome this drawback, Schmitz and Donalson [5] proposed a receptance coupling technique to predict the dynamic response at the tool tip. The technique allows coupling of analy- tical and/or experimental FRFs of individual components to get the response of the final assembly. In this first model, two components were joined just considering translational degrees of freedom, while the interface between them was considered flexible. The method was improved introducing the rotational degree of freedom related to bending with its joint flexibility value [6]. The mentioned joint conditions were determined correlating theoretical and experimental values and updating the flexibility values to obtain the best fitting. In recent years, several authors have proposed improvements to this method and have studied the influence of contact parameters [7–13]. Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/ijmactool International Journal of Machine Tools & Manufacture 0890-6955/$ - see front matter & 2014 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijmachtools.2013.12.002 n Corresponding author. Tel.: þ34 943 748000; fax: þ34 943 743800. E-mail addresses: imancisidor@ideko.es (I. Mancisidor), aurkiola@ideko.es (A. Urkiola), rafa.barcena@ehu.es (R. Barcena), jmunoa@ideko.es (J. Munoa), dombo@mm.bme.hu (Z. Dombovari), mzatarain@ideko.es (M. Zatarain). International Journal of Machine Tools & Manufacture 78 (2014) 18–29