Stochastic modeling of the cutting force in turning processes
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ORIGINAL ARTICLE
Stochastic modeling of the cutting force in turning processes ´ Gergo˝ Fodor1 · Henrik T Sykora2 · Daniel Bachrathy2 Received: 17 January 2020 / Accepted: 5 August 2020 / Published online: 25 September 2020 © The Author(s) 2020
Abstract The main goal of this study is to introduce a stochastic extension of the already existing cutting force models. It is shown through orthogonal cutting force measurements how stochastic processes based on Gaussian white noise can be used to describe the cutting force in material removal processes. Based on these measurements, stochastic processes were fitted on the variation of the cutting force signals for different cutting parameters, such as cutting velocity, chip thickness, and rake angle. It is also shown that the variance of the measured force signal is usually around 4–9% of the average value, which is orders of magnitudes larger than the noise originating from the measurement system. Furthermore, the force signals have Gaussian distribution; therefore, the cutting force model can be extended by means of a multiplicative noise component. Keywords Orthogonal cutting · Stochastic cutting force · Power spectrum · Noise
1 Introduction During material removal processes, machine tool vibrations can occur especially during roughing. It has a significant effect on the surface quality, tool life, and in extreme cases even the tool can be damaged. There are two main types of machine tool vibrations: chatter, which is a selfinduced oscillation caused by the surface regeneration effect [1]; and forced vibration, where the deviation in the cutting force is caused by the fast changes of the chip thickness, which can cause resonant vibrations in milling and interrupted turning processes. During the theoretical investigation of these vibrations, a widely used approach Gerg˝o Fodor
[email protected] Henrik T Sykora [email protected] D´aniel Bachrathy [email protected] 1
Department of Applied Mechanics, Budapest University of Technology and Economics, Budapest, Hungary
2
MTA-BME Lend¨ulet Machine Tool Vibration Research Group, Department of Applied Mechanics, Budapest University of Technology and Economics, Budapest, Hungary
is to describe the vibrations with deterministic delayed differential equations which can be utilized for linear stability analysis of, e.g., milling operations [2–5] as well as nonlinear analysis of milling operations [6, 7]. In these equations, the parameters (including the cutting force coefficients) are usually considered deterministic constants. During the measurement of the cutting force, large variations can be experienced (see Fig. 1), but these are usually attributed to the quality of the measurements and only the average force is considered the base for fitting the cutting parameters. However, these variations are orders of magnitude larger than being explained as a measurement noise. There are high-speed phenomena during cutting, such as chip fragmentation [8, 9], inhomogeneities in material quality [10–12], shear plane oscillation [1
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