Solution of Systems of Linear Delay Differential Equations Via Lambert Functions

Asl, Farshid Maghami; Ulsoy, A. Galip

doi:10.1115/detc2005-84076

Cited by 1 publication

(1 citation statement)

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“…Ulsoy et al [52,53] proposed the Lambert W function based method for machining stability anal-ysis. Butcher et al presented the Chebyshev polynomial based method [54] and Chebyshev collocation method [55] for milling stability prediction, respectively.…”

Section: Stability Analysis Methodsmentioning

confidence: 99%

On time-domain methods for milling stability analysis

Ding

Zhu

2012

Chin. Sci. Bull.

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As a basic and advanced machining technique, the high-speed milling process plays an important role in realizing the goal of high performance manufacturing. From the viewpoint of machining dynamics, obtaining chatter-free machining parameters is a prerequisite to guaranteeing machining accuracy and improving machining efficiency. This paper gives an overview on recent progress in time domain semi-analytical methods for chatter stability analysis of milling processes. The state of art methods of milling stability prediction in milling processes and their applications are introduced in detail. The bottlenecks involved are analyzed, and potential solutions are discussed. Finally, a brief prospect on future works is presented. High speed milling is widely utilized in manufacturing of complex surfaces for the fields of aerospace, ship, automotive, dies and molds etc., due to its advantage of obtaining high machining accuracy and high material removal rate with keeping low-amplitude cutting forces. Regarding to modeling of machining processes, the research topics on high speed milling can be categorized as: tool path planning, machining dynamics and machining physical modeling. Tool path planning is to plan the tool path according to the workpiece model, machining strategy and required machined error [1][2][3][4][5]. From the viewpoint of machining dynamics, the relative vibration between the workpiece and cutter in the milling process is the main reason of reducing product surface quality and limiting the production efficiency. To suppress the vibration impact by optimizing the machining parameters, the following two questions need to be addressed.(1) Stability analysis based on the dynamics of milling processes. As far as chatter vibrations are concerned, there are four different mechanisms: regeneration [6], mode coupling [7], friction [8] and thermo-mechanics of chip formation [9]. In milling processes, regenerative chatter is the most common form of self-excited vibration to reduce surface quality and machining efficiency [10,11]. The works on analysis of the stability of milling processes focus on calculating the stability boundary of the machining parameters based on the dynamic models characterizing the milling processes.(2) Machining accuracy analysis on the basis of stability analysis. Due to forced vibrations in milling processes, chatter-free machining parameters cannot ensure high performance machining. Vibration-induced surface errors can be classified as surface location error (SLE) [12] and surface roughness [13]. It is essential to take the stability and dynamical errors into account in machining optimization models to achieve high performance milling.

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