Proceedings of ASME 2016 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference IDETC 2016 August 21-24, 2016, Charlotte, North Carolina, USA IDETC2016-59940 SURFACE ERROR AND STABILITY CHART OF BEAM-TYPE WORKPIECE IN MILLING PROCESSES Adam K. Kiss Department of Applied Mechanics Budapest University of Technology and Economics Budapest, Hungary Email: kiss a@mm.bme.hu Daniel Bachrathy Department of Applied Mechanics Budapest University of Technology and Economics Budapest, Hungary Email: bachrathy@mm.bme.hu Gabor Stepan Department of Applied Mechanics Budapest University of Technology and Economics Budapest, Hungary Email: stepan@mm.bme.hu ABSTRACT In milling processes, the intermittent cutting force may lead to harmful vibrations. These vibrations are classiﬁed into two groups. One of them is the self excited vibration which comes from the loss of stability due to the regeneration effect and these vibrations lead to unacceptable chatter marks. The other one is the forced vibration which can lead to high Surface Location Error (SLE) in case of resonant spindle speeds. In this paper, the dynamics of the beam-type workpiece is considered which is modelled by means of Finite Element Analysis (FEA). Both the forced vibration and the stability properties are predicted along the tool path. The surface properties are computed on the stable regions of the stability chart which presents the chatter-free (sta- ble) parameter domain as a function of the spindle speed and the tool path. The theoretical results are compared to the measured SLE and surface roughness. 1 INTRODUCTION Eliminating the vibrations during milling process is an im- portant task, but unfortunately, it is unattainable in practice. The reason for this is two different types of vibration, which may oc- cur during the process. One of them is the self-excited vibration that is due to the loss of stability related to the surface regenera- tion effect [1]. The chip evolution is inﬂuenced by the subsequent position of the previous cutting edge and the current position of the current cutting edge [2]. This effect can be modelled with delay-differential equations (DDE) [3]. The other type of vibra- tion is the periodic forced vibration, but it plays a role only in the case if the machining process is stable. The forced vibration can be described by simple inhomogeneous ordinary differential equation (ODE) and it leads to large amplitude vibration in res- onant cases. From the mechanical point of view, the machining process is usually stable if the spindle frequency is close to the natural frequencies or its higher harmonics, however, large am- plitude resonant vibration can occur at these spindle speeds. The relative vibration between the milling tool and the workpiece re- sults a deviation between the machined and the desired surface, which also called as the Surface Location Error (SLE) [4, 5]. It is an essential role for a mechanical engineer to predict the behaviour of a milling process in order to achieve high material removal rate, thus increase the production rate in manufactur- ing. The stability properties is usually determined based on the so-called stability chart which presents the domain of the chatter- free (stable) technological parameter domain. It is usually repre- sented in the plane of the spindle speed and the axial immersion. It can be calculated by means of methods in time domain [6–8] or frequency domain also [9–11]. In time domain, the identiﬁ- cation of the modal parameters - which describe the dynamical behavior of the model - is required but it is complex engineer- ing procedure. An advantage of the frequency domain solutions is that they can directly use the measured Frequency Response Function (FRF). However, these FRF functions change in the work-space due to the different conﬁguration of the machine tool 1 Copyright c  2016 by ASME