Modelling of the stability of variable helix end mills

Turner, Sam; Merdol, Doruk; Altintaş, Yusuf; Ridgway, Keith

doi:10.1016/j.ijmachtools.2006.08.028

Cited by 95 publications

(41 citation statements)

References 11 publications

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“…The terms in (22) are: The schematic block diagram shown in Figure 4 can now be replaced by the mathematical model shown in Figure 6. Combining (20), (22) and (16) gives:…”

Section: State-space Formulationmentioning

confidence: 99%

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Analytical prediction of chatter stability for variable pitch and variable helix milling tools

Sims

Mann

Huyanan

2008

Journal of Sound and Vibration

178

120

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Regenerative chatter is a self-excited vibration that can occur during milling and other machining processes. It leads to a poor surface finish, premature tool wear, and potential damage to the machine or tool. Variable pitch and variable helix milling tools have been previously proposed to avoid the onset of regenerative chatter. Although variable pitch tools have been considered in some detail in previous research, this has generally focussed on behaviour at high radial immersions. In contrast there has been very little work focussed on predicting the stability of variable helix tools. In the present study, three solution processes are proposed for predicting the stability of variable pitch or helix milling tools.The first is a semi-discretisation formulation that performs spatial and temporal discretisation of the tool. Unlike previously published methods this can predict the stability of variable pitch or variable helix tools, at low or high radial immersions.The second is a time-averaged semi-discretisation formulation that assumes time-averaged cutting force coefficients. Unlike previous work, this can predict stability of variable helix tools at high radial immersion.The third is a temporal-finite element formulation that can predict the stability of variable pitch tools with a constant uniform helix angle, at low radial immersion.

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“…The terms in (22) are: The schematic block diagram shown in Figure 4 can now be replaced by the mathematical model shown in Figure 6. Combining (20), (22) and (16) gives:…”

Section: State-space Formulationmentioning

confidence: 99%

“…One exception is the work by Turner et al [22]. They proposed that variable helix tools could be modelled by taking the average pitch for each flute, and then applying the variable pitch stability analysis from reference [15].…”

Section: Introductionmentioning

confidence: 99%

Analytical prediction of chatter stability for variable pitch and variable helix milling tools

Sims

Mann

Huyanan

2008

Journal of Sound and Vibration

178

120

View full text Add to dashboard Cite

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“…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].…”

Section: Introductionmentioning

confidence: 99%

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

Tóth

Bachrathy

Stépàn

2016

Int J Adv Manuf Technol

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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

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“…To the authors' knowledge, only Turner [12], Sims [13] and Yusoff [14] considered the cases of variable helix angle in their studies. Sims proposed the tool could be discrete into a number of axial layers to solve the problem of variable helix angle.…”

Section: Introductionmentioning

confidence: 99%

Dynamics and stability predictions of variable helix milling

Xie¹

2015

Proceedings of the 2015 International Conference on Mechatronics, Electronic, Industrial and Control Engineering

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Abstract-In milling, it is important to research the stability lobes charts which determine stable regions where no chatter occurs. This paper presents the nonlinear model of milling considering the variable helix angle. Base on this model, an improved semi-discretization method is used to predict stability. Due to the delay between each flute varies along the axial depth of the tool in milling, the cutting tool is discrete into some axial layers to simplify calculate. The effects of variable helix angle and uniform helix angle on the corresponding stability charts are explored, it is revealed that many unstable islands arise in the low radial immersion ratio. However, as the radial immersion rates increase, variable helix angle has a little effect on stability. This fully shows that the helix angle plays an important impact for stability. Meantime this also confirms our proposed method can accurately capture unstable phenomenon at low radial immersion milling operations.

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Modelling of the stability of variable helix end mills

Cited by 95 publications

References 11 publications

Analytical prediction of chatter stability for variable pitch and variable helix milling tools

Analytical prediction of chatter stability for variable pitch and variable helix milling tools

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

Dynamics and stability predictions of variable helix milling

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