By C. Steve Suh
Presents new advancements on computing device software vibration regulate in keeping with discontinuous dynamical systems
Machining instability is a topical quarter, and there are a variety of guides that conceal the subject. despite the fact that, lots of those prior reviews have begun through assuming that the habit of the procedure should be linearised. in the meantime, there are numerous fresh advances within the fields of sign processing, nonlinear dynamics, and nonlinear keep an eye on, all of that are correct to the machining balance problem. This e-book establishes the basics of slicing mechanics and computing device instrument dynamics within the simultaneous time-frequency domain. the hot nonlinear keep an eye on thought built via the authors that allows simultaneous regulate of vibration amplitude within the time-domain and spectral reaction within the frequency-domain presents the basis for the improvement of a controller structure universally potential for the regulate of dynamic instability together with bifurcation and chaos. as soon as parameters underlying the coupling, interplay, and evolution of alternative slicing states and among the software and workpiece are proven, they could then be included into the structure to create a keep an eye on method that mitigate machining instability and allow powerful, chatter-free computing device device layout appropriate particularly to excessive pace micro- and nano-machining.
- Presents new advancements on computer software vibration keep watch over in line with discontinuous dynamical systems
- Provides a transparent and concise method of the knowledge and keep an eye on of laptop instrument and workpiece vibrations from an alternate view, contributing to an in-depth figuring out of slicing dynamics and powerful keep an eye on of machining instability
- Equips the reader with the information to appreciate the dynamics of slicing and operation of machine-tool platforms in several stipulations in addition to the idea that of slicing instability control
- Includes info examples in MATLAB coding
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Extra info for Control of Cutting Vibration and Machining Instability: A Time-Frequency Approach for Precision, Micro and Nano Machining
It was noted that cutting force amplitude oscillations were determined by the nonlinearity of the force, not by speed increments. It was also seen that both the tool and workpiece showed similar instability stages most of the time. However, when it was closer to the critical depth-of-cut, the cutting tool reached instability before the workpiece did. 00 mm, most of the time when the system was unstable, only the workpiece or the tool was unstable and not both. There were a few situations where both became unstable at the same time.
It was noted that in all cases where the tool was unstable, the tool was excited by the workpiece natural frequency and displayed broadband behavior. However, not all cases in which the tool was excited by the workpiece natural frequency were unstable. On the other hand, in almost all cases in which the workpiece was unstable, the workpiece had a broadband frequency component near the tool Cutting Dynamics and Machining Instability 31 natural frequency. This suggests the importance of considering the workpiece–tool coupling effect in modeling cutting dynamics.
66) The parameters a and b are called the dilation and translation parameters, respectively. In the equation below, the Gabor wavelet is given. 67) where γ is a positive constant. The Gabor wavelet function has been shown to offer the smallest time-frequency window of any wavelet , and therefore provides very high resolution in the joint time-frequency domain. The Gaussian part of this function provides a smooth, ﬁnite time window for the scalable sinusoidal function. It is also important to note that the Gabor wavelet function does not satisfy the continuous wavelet admissibility condition in a strict sense, but can be assumed satisfactory if γ is sufﬁciently large .