A simplified methodology for finding the natural frequencies and mode shapes of the machine tool structures Jatinder Garg a , Sonu Bala Garg b,⇑ a Baba Hira Singh BhattaI Institute of Engineering and Technology, Lehragaga 148133, Punjab, India b I.K. Gujral Punjab Technical University, Jalandhar 144603, Punjab, India article info Article history: Received 29 March 2020 Received in revised form 30 May 2020 Accepted 2 June 2020 Available online xxxx Keywords: Modal analysis Vibration analysis Machine tool structures Finite element method abstract Finding the natural frequencies of the machine tool structures is essential so that these can be kept away from the operational frequencies. Modelling and analysis of the actual structures is expensive and time- consuming. This paper presents a simplified, FEM based methodology for approximating the natural fre- quencies and mode shapes of the machine tools structures. This methodology was used to find the vibra- tion characteristics of a vertical milling machine under different loading conditions. The results showed that an increase in the mass of the workpiece, causes a decrease in its lower-order natural frequencies, but the higher-order natural frequencies remain largely unaffected. Ó 2020 Elsevier Ltd. All rights reserved. Selection and Peer-review under responsibility of the scientific committee of the 2nd International Con- ference on Future Learning Aspects of Mechanical Engineering. 1. Introduction Machine tools are important components of all the manufactur- ing systems. Vibration control of the machine tools is essential due to many reasons. Excessive vibrations spoil the surface finish and the dimensional accuracy of the products. They escalate wear and tear, promote loosening of the mating parts and reduce the tool life. Vibrations produce noise and chatter that adversely affect the health of the workers [1]. The most devastating effect of the vibration is observed when the frequency of external excitation coincides with the natural frequencies of the structure [2]. It trig- gers resonance, producing high scale deflection, that may lead to catastrophic failure. Therefore, it is essential to know the natural frequencies and the mode shapes of the structures [3]. The degrees of freedom of a structure decides the number of its natural frequencies. The machine tools structures are continuous systems. Therefore, they possess an infinite number of degrees of freedom. For the lightly damped structures, the lower order natural frequencies are the most dominant ones. Consequently, the knowl- edge of only these natural frequencies is sufficient for all practical purposes [4]. In the past, primarily the analytical techniques like Rayleigh’s method, Holzer’s method, and Experimental modal analysis were used for conducting the vibration analysis of the structures [5,6]. The availability of high-speed computers popularised the use of more powerful techniques like Finite Element Method (FEM) [7]. Several powerful commercial software like Ansys, Femap and IDEAS are available for conducting the FEM analysis. These software are quite expensive and require the development of a detailed model of the structure to be analysed. The machine tool structures are complex in shape due to the presence of many functional elements and parts. It makes their modelling and analysis time-consuming and expensive. Hence, It is logical to develop simplified methodologies by which the relevant proper- ties of the structures can be approximated quickly and economically. In the past various researchers tried to develop methodologies for the vibration analysis of the structures. Ba ˛ k and Jemielniak [8] developed a methodology and software for conducting the automatic modal analysis of the machine tools structures for novice machine operators. Mao [9] presented a complete method- ology for the operational modal analysis of the heavy machine tool structures. Luo et al. [10] proposed an active-excitation modal analysis based method for the dynamic analysis of the machine tools. Kumar et al. [11] tried to develop a FEM based methodology for the vibration analysis of the radial drilling machine structures. A simplified delamination modelling methodology was developed by Tan et al. [12] for tri-axial braided composites with macro- scale solid finite-element models. https://doi.org/10.1016/j.matpr.2020.06.022 2214-7853/Ó 2020 Elsevier Ltd. All rights reserved. Selection and Peer-review under responsibility of the scientific committee of the 2nd International Conference on Future Learning Aspects of Mechanical Engineering. ⇑ Corresponding author. E-mail address: sonugarg79@yahoo.com (S. Bala Garg). Materials Today: Proceedings xxx (xxxx) xxx Contents lists available at ScienceDirect Materials Today: Proceedings journal homepage: www.elsevier.com/locate/matpr Please cite this article as: J. Garg and S. Bala Garg, A simplified methodology for finding the natural frequencies and mode shapes of the machine tool struc- tures, Materials Today: Proceedings, https://doi.org/10.1016/j.matpr.2020.06.022