Robust prediction of chatter stability in milling based on the analytical chatter stability

Graham, Eldon; Mehrpouya, Majid; Park, Simon S.

doi:10.1016/j.jmapro.2013.08.005

Cited by 56 publications

(20 citation statements)

References 15 publications

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“…3. The intersection of the stability areas can be used as an approximation of the robust stability region [25]. See the resultant graph in Fig.…”

Section: Parameter Uncertaintymentioning

confidence: 99%

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Robust Stability Limit of Delayed Dynamical Systems

Bachrathy

2015

Period. Polytech. Mech. Eng.

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Keywords Robust stability, Multi-Dimensional Bisection Method (MDBM), turning, process damping IntroductionThe determination of the stability of dynamical systems with time delay is of high importance for many industrial and research applications. The investigation of the dynamics of turning processes is such a typical industrial problem. In order to reach high process efficiency the material removal rate (MRR) has to be maximized. The major limitation for increasing the MRR is the so-called chatter vibration. The origin of these self-excited vibrations is the surface regeneration effect, which can be described by linear delayed differential equations (DDEs) [1,2]. Another example is human balancing, which is often modelled by a simple inverted pendulum in the presence of reflex delay [3,4,5], which is a relevant issue to human motion control [6]. A similar problem is the remote control of periodic robotic motions, when the delay in the information transmission system is not negligible [7,8].The most important qualitative property of the corresponding dynamical system is the stability of the equilibrium or periodic motions. This is usually presented in the form of the socalled stability chart, that identifies those ranges of parameters where the linear system is stable.Many well-known computational techniques are available to determine the stability chart of DDEs [9,10,11,12,13,14].In many cases, especially for machining operations at low spindle speed, the computation of the stability boundary requires very high computational effort and unnecessarily high resolution, due to the dense and sharp line segments of the stability boundary (see Fig. 1). In these cases, the computation of the lower envelope of the dense stability lobe structure would be adequate.In case of time-domain computations [10,13,15,16,17], really high degree of discretization is required for proper results. In frequency domain computations [14,18,19,20], the determination of the very dense lobe structure in the unstable domain is unnecessary and also high resolution is required to determine the chatter frequency parameter, which is also a required computational step.Traditional computational methods consider exact models of the system, and do not take into account the uncertainty of

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“…3. The intersection of the stability areas can be used as an approximation of the robust stability region [25]. See the resultant graph in Fig.…”

Section: Parameter Uncertaintymentioning

confidence: 99%

“…These algorithms lead to numerically intensive computations with many limitations, hence the "robust formulation cannot accommodate more than two varying parameters due to increasing model complexity" [25].…”

Section: Introductionmentioning

confidence: 99%

Robust Stability Limit of Delayed Dynamical Systems

Bachrathy

2015

Period. Polytech. Mech. Eng.

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“…However, all these models assume that parameters of the milling process such as depth of cut, feed per tooth and cutting force are deterministic. Actually, these parameters are random in practical engineering due to uncertainty factors in real manufacturing environment, which would in turn influence the milling process (Sims et al, 2010;Graham et al, 2013;Hajdu et al, 2016). In this paper, a practical method is proposed to predict SLE in milling considering the effects of uncertain factors.…”

Section: Introductionmentioning

confidence: 99%

Prediction of surface location error in milling considering the effects of uncertain factors

et al. 2017

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Abstract. Machining accuracy of a milled surface is influenced by process dynamics. Surface location error (SLE) in milling determines final dimensional accuracy of the finished surface. Therefore, it is critical to predict, control, and minimize SLE. In traditional methods, the effects of uncertain factors are usually ignored during prediction of SLE, and this would tend to generate estimation errors. In order to solve this problem, this paper presents methods for probabilistic analysis of SLE in milling. A dynamic model for milling process is built to determine relationship between SLE and cutting parameters using full-discretization method (FDM). Monte-Carlo simulation (MCS) method and artificial neural network (ANN) based MCS method are proposed for predicting reliability of the milling process. Finally, a numerical example is used to evaluate the accuracy and efficiency of the proposed method.

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“…Common approaches to vibration control usually involve developed structures, applying passively or actively controlled friction dampers (Gaul and Becker, 2014;Zhang et al, 2014) or changing the working parameters of machines (Meehan, 2002;Bhogal et al, 2015). Some studies have focused on reliability computation (Viadero et al, 1994) and chatter reliability prediction of mechanical systems by taking the uncertainty of system parameters into account (Graham et al, 2013;Liu et al, 2016). However, in such approaches, the material of the mechanical structures is not fully exploited for reducing the dynamic response of structures.…”

Section: Introductionmentioning

confidence: 99%

A growth-based topology optimizer for stiffness design of continuum structures under harmonic force excitation

Yan

Hong

2016

J. Zhejiang Univ. Sci. A

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Abstract:The aim of this study is to explore the potential of various plant ramifications as concept generators for creating a brand topology optimization solution for stiffness design of continuum structures under harmonic force excitations. Firstly, a mathematical model is built to identify analytical laws that underlie the optimality of the effective but individual design rules of existing leaf venation morphogenesis. Then, a new evolutionary algorithm is developed to find the optimal topology of stiffened structures under harmonic force excitations. Candidate stiffeners are treated as being alive, growing at locations with a maximum displacement response gradient along the structural surface. Since the scale of the candidate stiffeners can be adaptively expanded or reduced during the simulation, computational resources could be saved, thereby enhancing the flexibility of topology optimization. Finally, the suggested approach is applied to a case study in which the displacement amplitude at specified locations is defined as the objective and the volume of added stiffeners as the constraint. The simulation process shows how the stiffness design of continuum structures can be conducted automatically using this bionic approach.

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Robust prediction of chatter stability in milling based on the analytical chatter stability

Cited by 56 publications

References 15 publications

Robust Stability Limit of Delayed Dynamical Systems

Robust Stability Limit of Delayed Dynamical Systems

Prediction of surface location error in milling considering the effects of uncertain factors

A growth-based topology optimizer for stiffness design of continuum structures under harmonic force excitation

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