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.
Highlights
During material removal processes, machine tool vibrations can occur especially during roughing
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
In case of multiplicative white noise intensity σw,1 computed from the parameter μ1 of the first-order filter, the results show a significant fluctuation with respect to the cutting parameters usually taking values between σw,1 = 0.1 and 1%, since μ1 behaves irregularly
Summary
Machine tool vibrations can occur especially during roughing. There are high-speed phenomena during cutting, such as chip fragmentation [8, 9], inhomogeneities in material quality [10,11,12], shear plane oscillation [13], rough surface of the workpiece, and friction. These phenomena play an important role in the amplitude of the forced vibrations, influencing the surface quality of the manufactured product and the detection of chatter [6, 14, 15]. The result of these methods is very sensitive to the values of the numerous and hardly measurable parameters, is often compromised by numerical difficulties, and is computationally very expensive
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