Time minimization of pocketing by zigzag passes along stability limit

Abstract

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.

Minimizing time of contour-parallel pocket end-milling by prescribing limit axial and radial depth pairs

“…By tracking the parameter combinations that ensure existence of the spectral radii of the monodromy matrix on the circumference of the unit circle, the stability limit that demarcates the stable and unstable spaces is determined. The process of tracking these critical parameter combinations on the plane of axial and radial depths is given as detailed flowchart in Ozoegwu et al 25…”

“…Existence of a coordinate for maximum limiting MRR ( MR R lim ) was identified and demonstrated to give minimum pocketing time for large pockets. The studies by Tekeli and Budak 22 and Ozoegwu and Ezugwu 24 considered one-way toolpath but Ozoegwu et al 25 have extended the optimization method to zigzag toolpath that maintains continuous contact between the tool and workpiece. The zigzag toolpath avoided the delay of return idle passes inherent in one-way toolpath thus hastening the pocketing process.…”

“…Bort et al 29 conducted – on the optimal control theory – a multi-objective optimization of productivity and surface quality and recorded for a case study reduction of the cycle time by 46% and the surface roughness (Ra) by 22%. This study aims at extending the optimization method of the works 22,24,25 using contour-parallel toolpath which also maintains continuous contact between the tool and workpiece like the zigzag toolpath. The contour-parallel toolpath maintains a single mode (up-milling or down-milling), while the zigzag toolpath changes mode from one pass to the next.…”

Development of Theoretical and Numerical Framework for Selecting the Cutting Process Parameters for Turned Slender Parts

“…These high-quality machined surfaces could be designed to control the direction of light propagation, effectively eliminating diffraction effects, and offering a qualitative analysis of optical component performance and improvements [26]. To identify the dominant errors affecting machining accuracy, a common approach involved removing the workpiece for offline measurement [27][28][29][30]. In this context, a measurement technique based on the double ball bar (DBB) was proposed to address geometric error measurement challenges for five-axis ultra-precision machine tools operating with interpolated five-axis motion [31].…”

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

“…The FDM, as applied in the stability analysis of milling, can be classified into two: the methods based on the interpolation theory [44][45][46][47][48][49] together with the more-time-saving methods based on the approximation (from the least squares sense) theory 50,51 and the methods based numerical integration which are further sub-divided into those based on Newton-Cotes method [52][53][54] and those based on spectral method. 55 The FDM has been applied in the study of different aspects of milling, for example, the least squares version has been applied 56,57 in minimizing pocketing time. Complete discretization method for prediction of milling stability was introduced by Li et al 58 The method not only discretizes the delayed state and the current state like the FDM but further discretizes other terms.…”