Wave attenuation effects on the chatter instability of end-milling

Advances in Mechanical Engineering

2018

Based on the full-discretization method, this work presents a generalized monodromy matrix as an exact function of the order of polynomial approximation of the milling state for chatter avoidance algorithm. In other words, the computational process is made smarter since the usual derivation of the monodromy matrices on order-by-order basis -a huge analytical involvement that rapidly gets heavier with a rise in the order of approximation -is bypassed. This is the highest possible level of generalization that seems to be the first of its kind among the time-domain methods as the known generalizations are limited to the interpolating/approximating polynomial of the milling state. It then became convenient in this work to study the stability of milling process up to the tenth order. More reliable methods of the rate of convergence analysis were suggested and utilized in consolidating the known result that the best accuracy of the fulldiscretization method lies with the third and fourth order. It is seen from numerical convergence analyses that, although accuracy most often decreases with rising order beyond the third-order methods, the trend did not persist with a continued rise in order.

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A general order full-discretization algorithm for chatter avoidance in milling

Advances in Mechanical Engineering

2018

“…The method is known for its marked reduction of computational time relative to the method of semi-discretization. The method of full-discretization has been applied in stability analysis of milling process from several perspectives: the methods based on interpolation theory [53][54][55][57][58][59], the methods based on approximation (from the least squares sense) theory [60][61][62] and the methods based on numerical integration which are divided into that based on NewtonCoates method [56] and that based on spectral method [63]. The method of full-discretization has been applied in analysis of advance milling models like mode coupling [64], spindle speed variation [65] and curvature effects [66,67].…”

Section: Introductionmentioning

confidence: 99%

Time minimization of pocketing by zigzag passes along stability limit

Int J Adv Manuf Technol

Ezugwu

2015

Pocketing with zigzag toolpath (which maintains near to continuous tool-workpiece contact) that is continuously optimized with limiting pairs of axial and radial depths is investigated in this work. Analysis led to a set of 16 conditional expressions eligible for description of pocketing time. An eligible expression becomes effective when all associated conditions are simultaneously met while the rest of the eligible expressions remain dormant until dimensions of pocket and tool favours another. Similar analysis has been carried out in other works for one-way toolpath which permits idle return passes and thus expected to incur delay. Comparison of zigzag and one-way toolpaths shows that the former always hastens pocketing operation because it better utilizes the stability limit of the system by maintaining continuously optimized to and fro passes. Numerical studies gives that zigzag toolpath can even half pocketing time of one-way toolpath for some choice of limiting process parameters. Similar to the conclusion that has been drawn for one-way toolpath in an earlier work it is seen that utilizing the coordinate of maximum limiting material removal rate (MRR lim ) for both down-and up-milling in a scheme of zigzag pocketing will not necessarily provide the minimum time because of geometrical constraints.

“…Experimental data of chatter and other vibrations in the turning and milling processes have been characterized using multi-scale methods (Litak, Syta, & Rusinek, 2011;Sen, Litak, Syta, & Rusinek, 2013) and flicker-noise spectroscopy (Litak, Polyakov, Timashev, & Rusinek, 2013). The theory of stabilizing wave attenuation effects in machining process was presented by Ozoegwu and Omenyi (2013). The theory posits that some of the force of interaction between the tool and workpiece acts normal to surface waves, thus depressing or flattening them in a way as to attenuate the chatter-causing regenerative effects.…”

Section: Introductionmentioning

confidence: 99%

“…The theory further posits that any variable of the attenuating force that varies in a way as to increase the amplitude of the attenuating force will suppress chatter instability. In Ozoegwu and Omenyi (2013), the wave attenuation theory was able to explain why chatter stability rises with rise in feed, fall in number of teeth and fall in hardness of workpiece material. The theory of stabilizing wave attenuation effects is being expanded in this work to cover the turning process.…”

Section: Introductionmentioning

confidence: 99%

Stabilizing wave attenuation effects in turning process

Production & Manufacturing Research

2014

Efforts have been made and continue to be made to understand the self-excited vibrations of machine tools called regenerative chatter. Theory of stabilizing wave attenuation effects in machining process presented in another work is expanded in this work to postulate the behaviour of turning stability lobes to changes in material, process and structural parameters. The wave attenuation theory simply stated that rise in attenuating forces suppresses chatter instability. Analysis in this work showed that rise in tool natural frequency x n , damping ratio n or feed speed v causes a rise in attenuating forces thus suppressing chatter. As expected from the wave attenuation theory harder workpiece materials with higher cutting coefficients C will better resist wave attenuation, and thus exhibit more chatter instability. Numerical verification of postulations is given.