Journal of Manufacturing Processes 14 (2012) 199–207 Contents lists available at SciVerse ScienceDirect Journal of Manufacturing Processes j ourna l ho me p age: www.elsevier.com/locate/manpro Technical paper Extending the inverse receptance coupling method for prediction of tool-holder joint dynamics in milling Mohammad Mahdi Rezaei ∗ , Mohammad R. Movahhedy, Hamed Moradi, Mohammad T. Ahmadian Center of Excellence in Design, Robotics and Automation (CEDRA), Department of Mechanical Engineering, Sharif University of Technology, Azadi Ave, Tehran, Iran a r t i c l e i n f o Article history: Received 4 April 2011 Received in revised form 3 October 2011 Accepted 21 November 2011 Available online 20 December 2011 Keywords: Inverse receptance coupling Joint model Tool-holder FRF Milling dynamics a b s t r a c t Recently, receptance coupling substructure analysis (RCSA) is used for stability prediction of machine tools through its dynamic response determination. A major challenge is the proper modelling of the substructures joints and determination of their parameters. In this paper, a new approach for predict- ing tool tip FRF is presented. First, inverse RCSA formulation is extended so that the holder FRFs can be identified directly through experimental modal tests. The great advantage of this formulation is its imple- mentation in arbitrary point numbers along joint length. Therefore, in comparison with previous inverse RCSA approaches, a more realistic joint model can be considered. In addition, due to applying the new approach, additional costly modal tests on the gauged tool are not required. This characteristic makes it possible to determine the holder FRFs without separating the tool; especially in situations where the holder end is inaccessible. The inclusion of joint parameters effect in the identified holder FRFs is another main advantage of such approach. Consequently, for identification of joint parameters, there is no need to use common error optimization based on fitting methods. The effect of overhang length is investigated through some analytical study and also experimental validation. Results show that the predicted tool tip FRF is exact in analytical case. Moreover, due to less noise effect, the predictions based on identified FRFs of longer tools are more accurate than the shorter ones (in experimental case). © 2011 The Society of Manufacturing Engineers. Published by Elsevier Ltd. All rights reserved. 1. Introduction Prediction and prevention of unstable chatter vibration is essential for achieving high quality and efficiency of machining processes. In the majority of methods used to find the stable free chatter regions of machining, finding the tool tip FRF is essential. End milling is one of the machining processes with most prone to the chatter. Budak and Altintas [1] presented a method to deter- mine the stability lobe diagram in milling using tool tip FRF. In practice, experimental modal analysis is used to determine the tool tip FRF. However, using this method is time consuming and cum- bersome, because the tool response changes as the tool is changed. In addition, for the cases where the experimental modal analysis is not possible such as flexible tools or micro milling, modelling is the only appropriate alternative. On the other hand, the modelling method based on only analytical results is a difficult task and often unreliable, especially for complex systems such as milling machine. An alternative is to couple the analytical response of the tool with the experimental response of the machine. ∗ Corresponding author. Tel.: +98 21 66165511; fax: +98 21 66000021. E-mail address: rezaei mm@mech.sharif.ir (M.M. Rezaei). The concept of receptance coupling has been extensively used for various applications. Wang and Liou [2] and Tsai and Chou [3] obtained the FRFs of a coupled system consisting of two planes from their separate FRFs. Ren and Beards [4] presented a more con- venient approach of receptance coupling for application in linear joint modelling. In recent year, many works have been devoted to apply the RCSA in prediction of tool tip FRF in machining. Schmitz et al. [5] used RCSA to predict the FRFs of tool-spindle system. In their work, FRFs of the tool was found by analytical methods and was coupled with the experimental FRF of tool holder tip to find the assembly FRF. In this way it is possible to find the FRF of the assembled system when the tool is changed, without repeti- tion of the experimental modal analysis. The main obstacle of this method is the joints modelling. Schmitz et al. [5] used a transla- tional spring/damper to model the joint and identified its value by fitting the results of the experimental test and modelling. Liu and Ewins [6] and Park et al. [7] showed that neglecting the rotational FRFs through coupling process produces a large error in (especially in predicting FRFs of long length tools [7]). However, measuring rotational FRFs is difficult and expensive. To extract the rotational FRFs of tool holder, they proposed the inverse RCSA method. In this method, the direct FRF of holder set is determined by experimen- tal modal test on gauged tool that has the same joint condition as the sample tool. Also, the tool rotational FRFs are identified through 1526-6125/$ – see front matter © 2011 The Society of Manufacturing Engineers. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.jmapro.2011.11.003