Applied M athematics 2013, 3(1): 1-11 DOI: 10.5923/j.am.20130301.01 Comparing up and Down Milling Modes of End-Milling Using Temporal Finite Element Analysis Chigbogu G. Ozoegwu * , Sam N. Omenyi, Sunday M. Ofochebe, Chinonso H. Achebe Department of Mechanical Engineering, Nnamdi Azikiwe University Awka, PMB 5025 Anambra state, Nigeria Abstract Two types of end milling at partial radial immersion are distinguished in this work, namely; up and down end-milling. They are theoretically given comparative study for a three tooth end miller operating at 0.5, 0.75 and 0.8 radial immersions. 0.5 and 0.8 radial immersion conditions are chosen so that analysis covers situations in which repeat and continuous tool engagements occur while 0.75 radial immersion just precludes tool free flight. It results from analysis that the down end-milling mode is better favoured for workshop application than the up end-milling mode from both standpoints of cutting force and chatter stability. This superiority in chatter stability is quantified by making use of the Simpson’s rule to establish that switching from up end-milling mode to down end-milling mode at 0.5 radial immersion almost doubles the possibility of chatter free milling while at 0.75 and 0.8 radial immersions this possibility almost triples. This result conforms to the age long recognition from workshop practices that climb milling operations are much more stable than conventional milling operations. Validation of the resulting stability charts is conducted via MATLAB dde23 time domain numerical analysis of selected points on the parameter plane of spindle speed and depth of cut. Keywords Up end-milling, Down End-milling, Temporal Finite Elements, Phase Trajectories, Simpson’s Rule 1. Introduction Machining is needed for the production of specialized components in the aerospace, marine, automobile and other industries. For this reason best mode of machining is sought after for best productivity and quality of components. Among other methods of machining, end milling is extensively used in the industry. In end milling a machined surface that is at right angle with the cutter axis results as shown Figure 1. Milling cutters equipped with shanks for mounting on the spindle are utilized for end milling. Two types of end-milling at partial radial immersion are distinguished as shown in figure 2. Milling operation as depicted in figure 2.a dynamically looks like the conventional milling since workpiece feed is in opposite direction to cutter rotation at advent of tooth-workpiece engagement. Chip thickness progressively grows from zero to non-zero values as feed progresses in this type of milling. The end milling process of figure 2.b dynamically resembles the climb milling being that workpiece feed is in the same direction as cutter rotation at inception of a tooth-workpiece engagement. Chip thickness starts from non-zero value and ends at zero value in this type of milling. These milling processes will thus be referred to in this work as up end-milling and down end-milling respectively. Radial * Corresponding author: chigbogug@yahoo.com (Chigbogu G. Ozoegwu) Published online at http://journal.sapub.org/am Copyright © 2013 Scientific & Academic Publishing. All Rights Reserved immersion  is defined for these milling processes to mean the ratio of the radial depth of cut to the tool diameter. The aim here is to compare the cutting forces and stability of both types of end milling process for a three tooth milling tool at half, three-quarters and four-fifths radial immersions. The first major difference between this work and others is that the cutting force of the non-chattered down end-milling and up end-milling are compared. It is suggested that there is less possibility of fatigue in the down end-milling mode since its magnitude of unperturbed cutting force is always less than that of the up end-milling at all radial immersions. The superiority of conventional milling over climb milling in terms of surface quality of component in workshop practice is long known and documented[1-3]. It is noted by Joshi[2] that conventional milling has fixture or clamping problems that is entirely absent in climb milling. This is due to the lift effect cutting forces have on the workpiece in conventional milling. Miller and Miller[3] wrote that climb milling allows faster material removal rate and surface finish than conventional milling. The poorer surface finish in conventional milling is attributed to tooth-workpiece rubbing that occurs before active engagement. The fixture and rubbing-induced surface problem of conventional milling are not expected in up end-milling since the machined surface is at right angle with the cutter axis. The dynamic resemblance of up and down end-milling with conventional and climb milling respectively is considered to mean resemblance in stability. Analysis shows that domain of chatter stability of down milling mode is much greater than that of up milling mode at all the studied