Effect of wavy tool path on the stability properties of milling by the implicit subspace iteration method

Abstract

There are several practical methods to reduce machine tool vibrations that have negative effects especially on the quality of the machined surface. The most intricate vibration is the regenerative one originated in a delay effect of cutting processes. One group of the methods that may be successful in avoiding regenerative vibrations is the appropriate variation of the corresponding time delay. This study presents the stability analysis of milling processes in case of an especially intricate way of varying the delay in time: the radial depth of cut is varied in face milling resulting in a wavy tool path. The combination of the semidiscretization method and the implicit subspace iteration method is introduced to present an efficient way of calculating stability charts that provide conclusions regarding the use of this method in eliminating chatter.Keywords: chatter; wavy tool path; implicit subspace iteration; semi-discretization IntroductionMachine tool chatter has a negative effect on the lifetime of the machine tools and on the quality of the surface finish of the workpiece [1][2][3][4]. This self-excited vibration is originated in the so-called surface regeneration effect [3][4][5]. The mathematical modeling of chatter is rooted in the theory of delay differential equations (DDEs) [6], and the primary cause of instability is the presence of a large time delay in the cutting processes.A constant single point delay appears in the DDE of the commonly used mechanical models of milling processes at constant spindle speed if conventional helical tools with even pitch angles are used. The time delays are proportional to the pitch angles between two neighboring cutting edges, and inversely proportional to the spindle speed.Different tool geometries and operating conditions have been developed in order to improve the stability properties of cutting processes by weakening the negative effect of the inherent time delay by disturbing the concentrated nature of the delayed term in the corresponding equations of motion.In case of milling processes, the concentrated nature of the time delay can be changed to a more disturbed one by introducing uneven pitch angles between the cutting edges [7,8,9,10]. This idea results in multiple discrete time delays in the system, whose number depends on the number of teeth of the tool and the applied pitch angle distribution [11,12,13].Milling tools with varying helix angle [14,15,16,17,10] or with wavy cutting edges [18,19] are used to achieve a similar effect by distributing the concentrated time delay even further to continuously varying delays over a given delay-interval. In these cases, the pitch angles are changing continuously along the axial coordinate of the tool, which leads to DDE models with distributed time delays [20]. In addition to the continuously varying

Ensuring the chatter stability of milling by optimizing the workpiece stock

“…The choice of the target value of the goal function for the proposed optimization approach is based on experience and results obtained from the investigation of the influence of dynamic characteristics of the "tool-workpiece" system on stability margins at steady-state milling motion. For example, in [14], [15], it was established that increasing eigenfrequency, stiffness, and modal damping of the systems leads to the shift of stability margins in the direction of increasing spindle speed and axial cutting depth.…”

“…Using an alternative representation of the stability diagram allows demonstrating the position of stability margins near zones where the dimensionless frequency is even = 1, 2 … [15]. Given the superposition principle for the increased number of DOFs, one can formulate the milling vibration stability criterion, that ensures at certain values of the spindle speed the superimposition of stability zones associated with the and natural frequencies of the workpiece:…”

Performance of wiper geometry carbide tools in face milling of AISI 1045 steel

“…Vibrations with excessive amplitudes can cause various disorders in the machining processes, such as reduction in the cutting tool life, tool breakage, worsening of the workpiece surface quality and even, in extreme cases, damage the machine tool spindle. Thus, the search for milling conditions to provide lower vibration and, consequently, better surface finish and integrity has been the target of the works of several researchers (Altintas [13], Jawaid et al [17], Richetti et al [18], Agic et al [19] and Toth et al [20]).…”