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

Abstract

The purpose of this study is to minimize pocketing time by exploiting the most beneficial aspects of tool dynamics and the most beneficial chronology of tool passes in contour-parallel toolpath. This is achieved by always prescribing limiting axial and radial depth pairs on a contour-parallel toolpath as a means of minimizing pocketing time within milling machine load specifications. The optimization approach is identified to be of two types: boundary to centre ( b→ c) execution and centre to boundary ( c→ b) execution. Expression for pocketing time is developed for each type taking into account the revelation that the lengths of the bivariately optimized cyclic passes between the first and last cycles constitute an arithmetic series. The presented expressions are demonstrated to be useful in systematic determination of choice of progression (either ( b→ c) execution or ( c→ b) execution) of contour-parallel pocketing operation and choice of limiting axial and radial depth pairs that guarantee minimum machining time. For example, the studied experimentally characterized case gave that ( c→ b) execution is more time saving than ( b→ c) execution by about 3.5565%–15.7690%. This experimentally characterized case also confirms the expectation that continuous tool–workpiece contact of contour-parallel toolpath always ensures a shorter pocketing time than both one-way up- and down-milling toolpaths. It is further seen that it is faster pocketing at high radial depth range of 60%–100% of tool diameter which fortunately is the range of less load restrictions. The benefits of contour-parallel toolpath relative to one-way up- and down-milling toolpaths got more strongly confirmed when the pocket got larger (for example, the time saving of ( c→ b) execution relative to one-way up-milling attained 51.6733% for a larger pocket, while time saving of 41.3385% was recorded for smaller pocket) and when the slope of limiting radial depth versus axial depth got less.