Stability of Interrupted Cutting by Temporal Finite Element Analysis

Bayly, Philip V.; Halley, Jeremiah E.; Mann, Brian P.; Davies, Matthew A.

doi:10.1115/1.1556860

Cited by 339 publications

(137 citation statements)

References 9 publications

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“…Altintas and Budak proposed a linear model for spindle-tool chatter avoidance using the single-frequency and the multi-frequency methods to solve the stability problem [9,10]. Alternative algorithms such as semi-discretization, temporal finite elements analysis or Chebyshev collocation methods, allow a faster obtention of the flip lobes [11][12][13][14]. What is more, these methods can take into account several nonlinearities as the variation of the modal parameters of the system, or the variation of the geometry or the cutting coefficients of the tool.…”

Section: Introductionmentioning

confidence: 99%

Chatter avoidance in the milling of thin floors with bull-nose end mills: Model and stability diagrams

Campa

Lacalle

Celaya

2011

International Journal of Machine Tools and Manufacture

120

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The milling of thin parts is a high added value operation where the machinist has to face the chatter problem. The study of the stability of these operations is a complex task due to the changing modal parameters as the part losses mass during the machining and the complex shape of the tools that are used. The present work proposes a methodology for chatter avoidance in the milling of flexible thin floors with a bull-nose end mill. First, a stability model for the milling of compliant systems in the tool axis direction with bullnose end mills is presented. The contribution is the averaging method used to be able to use a linear model to predict the stability of the operation. Then, the procedure for the calculation of stability diagrams for the milling of thin floors is presented. The method is based on the estimation of the modal parameters of the part and the corresponding stability lobes during the machining. As in thin floor milling the depth of cut is already defined by the floor thickness previous to milling, it is proposed the use of stability diagrams that relate the tool position along the tool-path with the spindle speed. Hence, the sequence of spindle speeds that the tool must have during the milling can be selected. Finally, this methodology has been validated by means of experimental tests.

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Section: Introductionmentioning

confidence: 99%

Chatter avoidance in the milling of thin floors with bull-nose end mills: Model and stability diagrams

Campa

Lacalle

Celaya

2011

International Journal of Machine Tools and Manufacture

120

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show abstract

“…There have been many algorithms [30,38,39,40] developed during the last 15 years for systems where the time-delay effect is coupled with parametric excitation. The semidiscretization method (SDM) is one of the efficient ways to analyze stability [20,41,42,43,30,31,32].…”

Section: Brief Summary Of the Semi-discretization Methodsmentioning

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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“…In the last decade, a few numerical methods have been proposed to address the study of the asymptotic stability of time periodic delay systems including time finite element analysis (Bayly et al , 2001), numerical simulation (Zhao and Balachandran, 2001), statistical signal variance (Schmitz et al , 2002), harmonic balance and infinite determinants (Budak and Altintas, 1998), approximation of the delay by weighted integrals and semi-discretization method (Insperger and Stepan, 2004). Other interesting papers are (Szalai et al , 2006;Verheyden et al , 2005).…”

Section: Introductionmentioning

confidence: 99%

Numerical Computation of Characteristic Multipliers for Linear Time Periodic Coefficients Delay Differential Equations

Breda

Maset

Vermiglio

2006

IFAC Proceedings Volumes

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Stability of Interrupted Cutting by Temporal Finite Element Analysis

Cited by 339 publications

References 9 publications

Chatter avoidance in the milling of thin floors with bull-nose end mills: Model and stability diagrams

Chatter avoidance in the milling of thin floors with bull-nose end mills: Model and stability diagrams

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

Numerical Computation of Characteristic Multipliers for Linear Time Periodic Coefficients Delay Differential Equations

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