A Coupled Theoretical-Experimental Dynamical Model for Chatter Prediction in Milling Processes

2009 ◽  
Author(s):  
Giuseppe Catania ◽  
Nicolo` Mancinelli
Keyword(s):  
High Speed ◽  
Lumped Parameter Model ◽  
Milling Machine ◽  
Beam Shape ◽  
Milling Operations ◽  
Excited Vibration ◽  
Modal Model ◽  
Cutting Force Components ◽  
The Stability ◽  
Delay Differential

Productivity of high speed milling operations can be seriously limited by chatter occurrence. Several studies on this self-excited vibration can be found in the literature: simple models (1 or 2 dofs) are proposed, i.e. a lumped parameter model of the milling machine being excited by regenerative, time-varying cutting forces. In this study, a model of the milling machine is proposed: the machine frame and the spindle were modeled by an experimentally evaluated modal model, while the tool was modeled by a discrete modal approach, based on the continuous beam shape analytical eigenfunctions. The regenerative cutting force components lead to a set of Delay Differential Equations (DDEs) with periodic coefficients; DDEs were numerically integrated for different machining conditions. The stability lobe charts were evaluated using the semi-discretization method [6–7] that was extended to n dofs models (with n >2). Differences between the stability charts obtained by the low dofs models and the stability charts obtained by the new n dofs model are pointed out. Time histories and spectra related to the vibratory behavior of the system were numerically obtained to verify the effectiveness of the stability charts obtained with the n dofs modal model.

Chatter Vibration Modeling in High Speed Milling Operations

2008 ◽  
Author(s):  
Giuseppe Catania ◽  
Nicolo` Mancinelli
Keyword(s):  
High Speed ◽  
Removal Rate ◽  
Lumped Parameter Model ◽  
Beam Shape ◽  
Stability Lobe ◽  
Milling Operations ◽  
Excited Vibration ◽  
Cutting Force Components ◽  
The Stability ◽  
High Removal Rate

High removal rate in milling operations can be limited by chatter occurrence. Several studies on this self-excited vibration can be found in the literature: simple models (1 or 2 dofs) are proposed, i.e. a lumped parameter model of the milling machine being excited by regenerative, time-varying cutting forces. In this study, the machine tool spindle was modeled by a discrete modal approach, based on the continuous beam shape, analytical eigenfunctions, while the eigenvalues were mainly experimentally identified. The regenerative cutting force components lend to a set of Delay Differential Equations (DDEs) with periodic coefficients; DDEs were numerically integrated for different machining conditions. The stability lobe chart was evaluated using the semi-discretization method. Time histories, spectra and Poincare´ maps related to the vibratory behavior of the system were numerically obtained and differences with respect to the bifurcations predicted by the simplest models known in literature are pointed out. Some different behaviors in the shape of the stability lobe charts and in the spectra of the chatter vibrations were also observed.

Stability of Milling Operations With Asymmetric Cutter Dynamics in Rotating Coordinates

2016 ◽  
Vol 138 (8) ◽  
Author(s):  
Alptunc Comak ◽  
Orkun Ozsahin ◽  
Yusuf Altintas
Keyword(s):  
Time Domain ◽  
Machine Tools ◽  
High Speed ◽  
End Mill ◽  
Spindle Shaft ◽  
Milling Operations ◽  
Stability Model ◽  
Principal Directions ◽  
The Stability ◽  
Rotating Coordinates

High-speed machine tools have parts with both stationary and rotating dynamics. While spindle housing, column, and table have stationary dynamics, rotating parts may have both symmetric (i.e., spindle shaft and tool holder) and asymmetric dynamics (i.e., two-fluted end mill) due to uneven geometry in two principal directions. This paper presents a stability model of dynamic milling operations with combined stationary and rotating dynamics. The stationary modes are superposed to two orthogonal directions in rotating frame by considering the time- and speed-dependent, periodic dynamic milling system. The stability of the system is solved in both frequency and semidiscrete time domain. It is shown that the stability pockets differ significantly when the rotating dynamics of the asymmetric tools are considered. The proposed stability model has been experimentally validated in high-speed milling of an aluminum alloy with a two-fluted, asymmetric helical end mill.

Investigation of Gyroscopic Effect on the Stability of High Speed Micromilling via Bifurcation Analysis

2021 ◽  
Vol 5 (4) ◽  
pp. 130
Author(s):  
Rinku K. Mittal ◽  
Ramesh K. Singh
Keyword(s):  
High Speed ◽  
Degrees Of Freedom ◽  
Multistep Method ◽  
Gyroscopic Effect ◽  
High Rotational Speed ◽  
Micro Tool ◽  
The Stability ◽  
Delay Differential ◽  
Stability Limits ◽  
Micro Tools

Catastrophic tool failure due to the low flexural stiffness of the micro-tool is a major concern for micromanufacturing industries. This issue can be addressed using high rotational speed, but the gyroscopic couple becomes prominent at high rotational speeds for micro-tools affecting the dynamic stability of the process. This study uses the multiple degrees of freedom (MDOF) model of the cutting tool to investigate the gyroscopic effect in machining. Hopf bifurcation theory is used to understand the long-term dynamic behavior of the system. A numerical scheme based on the linear multistep method is used to solve the time-periodic delay differential equations. The stability limits have been predicted as a function of the spindle speed. Higher tool deflections occur at higher spindle speeds. Stability lobe diagram shows the conservative limits at high rotational speeds for the MDOF model. The predicted stability limits show good agreement with the experimental limits, especially at high rotational speeds.

A New Curve Tracking Algorithm for Efficient Computation of Stability Boundaries of Cutting Processes

2007 ◽  
Vol 2 (4) ◽  
pp. 360-365 ◽  
Author(s):  
Christoph Henninger ◽  
Peter Eberhard
Keyword(s):  
Stability Boundary ◽  
Computational Cost ◽  
Boundary Curve ◽  
Efficient Computation ◽  
Technological Parameters ◽  
Excited Vibration ◽  
The Stability ◽  
Cutting Processes ◽  
Delay Differential ◽  
Curve Tracking

Dynamic stability of cutting processes such as milling and turning is mainly restricted by the phenomenon of the regenerative effect, causing self-excited vibration, which is well known as machine-tool chatter. With the semidiscretization method for periodic delay-differential equations, there exists an appropriate method for determining the stability boundary curve in the domain of technological parameters. The stability boundary is implicitly defined as a level set of a function on the parameter domain, which makes the evaluation computationally expensive when using complete enumeration. In order to reduce computational cost, we first investigate two types of curve tracking algorithms finding them not appropriate for computing stability charts as they may get stuck at cusp points or near-branch zones. We then present a new curve tracking method, which overcomes these difficulties and makes it possible to compute stability boundary curves very efficiently.

scholarly journals Milling Stability Prediction with Multiple Delays via the Extended Adams-Moulton-Based Method

2017 ◽  
Vol 2017 ◽  
pp. 1-15 ◽  
Author(s):  
Jianfeng Tao ◽  
Chengjin Qin ◽  
Chengliang Liu
Keyword(s):  
Transition Matrix ◽  
Rotation Period ◽  
Small Time ◽  
Multiple Delays ◽  
Stability Prediction ◽  
Regenerative Chatter ◽  
Milling Stability ◽  
Milling Operations ◽  
The Stability ◽  
Delay Differential

The occurrence of machining chatter may undermine the workpiece surface quality, accelerate the tool wear, and even result in serious damage to the machine tools. Consequently, it is of great importance to predict and eliminate the presence of such unstable and detrimental vibration. In this paper, we present an extended Adams-Moulton-based method for the stability prediction of milling processes with multiple delays. Taking the nonuniform pitch cutters or the tool runout into account, the regenerative chatter for milling operations can be formulated as delay differential equations with multiple delays. The dynamics model for milling regenerative chatter is rewritten in the state-space form. Dividing the spindle rotation period equally into small time intervals, the delay terms are approximated by Lagrange interpolation polynomials, and the Adams-Moulton method is adopted to construct the Floquet transition matrix. On this basis, the milling stability can be derived from the spectral radius of the transition matrix based on Floquet theory. The calculation efficiency and accuracy of the proposed algorithm are verified through making comparisons with the semidiscretization method (SDM) and the enhanced multistage homotopy perturbation method (EMHPM). The results show that the proposed method has both high computational efficiency and accuracy.

Stability-Based Spindle Design Optimization

2006 ◽  
Vol 129 (2) ◽  
pp. 407-415 ◽  
Author(s):  
Vincent Gagnol ◽  
Belhassen C. Bouzgarrou ◽  
Pascal Ray ◽  
Christian Barra
Keyword(s):  
High Speed ◽  
Modal Identification ◽  
Design Parameters ◽  
Depth Of Cut ◽  
Chatter Vibration ◽  
High Rotational Speed ◽  
Milling Operations ◽  
Critical Requirement ◽  
The Stability ◽  
Gyroscopic Coupling

Prediction of stable cutting regions is a critical requirement for high-speed milling operations. These predictions are generally made using frequency-response measurements of the tool-holder-spindle set obtained from a nonrotating spindle. However, significant changes in system dynamics occur during high-speed rotation. In this paper, a dynamic high-speed spindle-bearing system model is elaborated on the basis of rotor dynamics prediction and readjusted on the basis of experimental modal identification. The dependency of dynamic behavior on speed range is then investigated and determined with accuracy. Dedicated experiments are carried out in order to confirm model results. They show that dynamic effects due to high rotational speed and elastic deformations, such as gyroscopic coupling and spin softening, have a significant influence on spindle behavior. By integrating the modeled speed-dependent spindle transfer function in the chatter vibration stability approach of Altintas and Budak (1995, CIRPS Ann, 44(1), pp. 357–362), a new dynamic stability lobe diagram is predicted. Significant changes are observed in the stability limits constructed using the proposed approach and allow accurate prediction of cutting conditions to be established. Finally, optimization studies are performed on spindle design parameters in order to obtain a chatter vibration-free cutting operation at the desired speed and depth of cut for a given cutter.

Self-excited Vibration Control of the Flexible Planar Parallel 3-RRR Robot

2018 ◽  
Vol 25 (2) ◽  
pp. 351-361
Author(s):  
Zhi-cheng Qiu ◽  
Jie Yang ◽  
Xian-min Zhang
Keyword(s):  
High Speed ◽  
Parallel Robot ◽  
The Self ◽  
Flexible Robot ◽  
Nonlinear Controller ◽  
Control Approach ◽  
Excited Vibration ◽  
Improve Accuracy ◽  
The Stability ◽  
Fuzzy Control Algorithm

A self-excited vibration active control approach for a 3-RRR flexible planar parallel robot is developed to improve accuracy and stability. The 3-RRR parallel flexible robot experimental setup is constructed. From the motion experiments, it is demonstrated that the residual vibration can be converted to self-excited vibration at a high-speed motion, which will affect the stability and positioning precision of the platform. To suppress the self-excited vibration owing to flexibility, friction, backlash, coupling, and other nonlinear factors, a nonlinear controller and a fuzzy control algorithm are designed to attenuate the self-excited vibration. Experiments are conducted in different positions of the 3-RRR flexible parallel robot. The experimental results demonstrate that the investigated control methods can suppress the self-excited vibration effectively.

The Analysis of Self-Excited Vibration in Processing System of Single Blade Rigid Boring Reamer

2014 ◽  
Vol 945-949 ◽  
pp. 761-765
Author(s):  
Zhen Dong ◽  
Xing Quan Shen
Keyword(s):  
High Speed ◽  
Processing System ◽  
Common Phenomenon ◽  
Deep Processing ◽  
High Speed Cutting ◽  
Excited Vibration ◽  
Precision Hole ◽  
The Stability ◽  
The Impact ◽  
Hole Machining

The reaming process with rigid single blade reamers boring is one kind of deep processing methods which develop rapidly in recent years,which has a series of advantages such as high-speed cutting, auto-oriented, low surface roughness and so on.Appear as one kind of precision hole processing technology in the deep hole processing currently,and shows the superiority of processing.The self-excited vibration is a common phenomenon in deep processing,and seriously affect the stability of hole machining and processing quality.It performance very obvious in rigid single blade reamers boring processing,and has a certain degree of particularity. Established as a mathematical model of the rigid boring reamerThe analysis of mechanism of Self-excited vibration in reaming processing of single blade rigid boring reamer, and the study the impact of the friction characteristics of the guide block and the hole in self-excited vibrations,provide the basis for the inhibition of self-excited vibration.

Integration of Drill Torsional-Axial Coupling in Spindle-Vibratory Drilling Head Model for Stability Analysis

2013 ◽  
Author(s):  
Said Mousavi ◽  
Vincent Gagnol ◽  
Pascal Ray
Keyword(s):  
High Speed ◽  
Design Parameters ◽  
Head Model ◽  
Machining Processes ◽  
Alternative Response ◽  
Analytical Stability ◽  
Stability Lobes ◽  
Excited Vibration ◽  
The Stability ◽  
Industrial Solutions

The drilling of deep holes with small diameters remains an unsatisfactory technology, since its productivity is rather limited. The main limit to an increase in productivity is directly related to the poor chip evacuation, which induces frequent tool breakage and poor surface quality. Retreat cycles and lubrication are common industrial solutions, but they induce productivity and environmental drawbacks. An alternative response to the chip evacuation problem is the use of a vibratory drilling head, which enables the chips to be fragmented thanks to the axial self-excited vibration. Contrary to conventional machining processes, axial drilling instability is sought, thanks to an adjustment of head design parameters and appropriate conditions of use. In this paper, self-vibratory cutting conditions are established through a specific stability lobes diagram. A dynamic high-speed spindle / drilling head / tool system model is elaborated on the basis of rotor dynamics predictions. The model-based tool tip FRF is integrated into an analytical stability approach. The torsional-axial coupling of the twist drill is investigated and consequences on drilling instability are established. Specific stability lobes are established and indicate modifications of self-excited operating zones. This approach allows refining the stability prediction of the global system during a drilling operation.

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