scholarly journals Estimation of the Bistable Zone for Machining Operations for the Case of a Distributed Cutting-Force Model

2016 ◽  
Vol 11 (5) ◽  
Author(s):  
Tamás G. Molnár ◽  
Tamás Insperger ◽  
S. John Hogan ◽  
Gábor Stépán
Keyword(s):  
Cutting Force ◽  
Distributed Delay ◽  
Nonlinear Function ◽  
Force Model ◽  
Center Manifold Reduction ◽  
Stability Boundaries ◽  
Force System ◽  
Bistable Region ◽  
The Stability ◽  
Machining Operations

Regenerative machine tool chatter is investigated for a single-degree-of-freedom model of turning processes. The cutting force is modeled as the resultant of a force system distributed along the rake face of the tool, whose magnitude is a nonlinear function of the chip thickness. Thus, the process is described by a nonlinear delay-differential equation, where a short distributed delay is superimposed on the regenerative point delay. The corresponding stability lobe diagrams are computed and are shown numerically that a subcritical Hopf bifurcation occurs along the stability boundaries for realistic cutting-force distributions. Therefore, a bistable region exists near the stability boundaries, where large-amplitude vibrations (chatter) may arise for large perturbations. Analytical formulas are obtained to estimate the size of the bistable region based on center manifold reduction and normal form calculations for the governing distributed-delay equation. The locally and globally stable parameter regions are computed numerically as well using the continuation algorithm implemented in dde-biftool. The results can be considered as an extension of the bifurcation analysis of machining operations with point delay.

scholarly journals Investigating Multiscale Phenomena in Machining: The Effect of Cutting-Force Distribution Along the Tool’s Rake Face on Process Stability

2015 ◽  
Author(s):  
Tamás G. Molnár ◽  
Tamás Insperger ◽  
S. John Hogan ◽  
Gábor Stépán
Keyword(s):  
Cutting Force ◽  
Distributed Delay ◽  
Chip Thickness ◽  
Rake Face ◽  
Center Manifold Reduction ◽  
Force System ◽  
Force Magnitude ◽  
Stability Lobe ◽  
The Stability ◽  
Stability Limits

Regenerative machine tool chatter is investigated in a nonlinear single-degree-of-freedom model of turning processes. The nonlinearity arises from the dependence of the cutting-force magnitude on the chip thickness. The cutting-force is modeled as the resultant of a force system distributed along the rake face of the tool. It introduces a distributed delay in the governing equations of the system in addition to the well-known regenerative delay, which is often referred to as the short regenerative effect. The corresponding stability lobe diagrams are depicted, and it is shown that a subcritical Hopf bifurcation occurs along the stability limits in the case of realistic cutting-force distributions. Due to the subcriticality a so-called unsafe zone exists near the stability limits, where the linearly stable cutting process becomes unstable to large perturbations. Based on center-manifold reduction and normal form calculations analytic formulas are obtained to estimate the size of the unsafe zone.

Analysis of Cutting Force in Elastomer End-Milling

2017 ◽  
Vol 11 (6) ◽  
pp. 958-963
Author(s):  
Koji Teramoto ◽  
◽  
Takahiro Kunishima ◽  
Hiroki Matsumoto
Keyword(s):  
Parameter Identification ◽  
Cutting Force ◽  
Cutting Forces ◽  
End Milling ◽  
Process Models ◽  
Force Model ◽  
Cutting Force Model ◽  
Cutting Force Prediction ◽  
Force Prediction ◽  
The Stability

Elastomer end-milling is attracting attention for its role in the small-lot production of elastomeric parts. In order to apply end-milling to the production of elastomeric parts, it is important that the workpiece be held stably to avoid deformation. To evaluate the stability of workholding, it is necessary to predict cutting forces in elastomer end-milling. Cutting force prediction for metal workpiece end-milling has been investigated for many years, and many process models for end-milling have been proposed. However, the applicability of these models to elastomer end-milling has not been discussed. In this paper, the characteristics of the cutting force in elastomer end-milling are evaluated experimentally. A standard cutting force model and its parameter identification method are introduced. By using this cutting force model, measured cutting forces are compared against the calculated results. The comparison makes it clear that the standard cutting force model for metal end-milling can be applied to down milling for a rough evaluation.

Stability Predictions for End Milling Operations With a Nonlinear Cutting Force Model

2009 ◽  
Vol 131 (6) ◽  
Author(s):  
Alex Elías-Zúñiga ◽  
Jovanny Pacheco-Bolívar ◽  
Francisco Araya ◽  
Alejandro Martínez-López ◽  
Oscar Martínez-Romero ◽  
...  
Keyword(s):  
Experimental Data ◽  
Cutting Force ◽  
End Milling ◽  
Stability Conditions ◽  
Force Model ◽  
Process Stability ◽  
Cutting Force Model ◽  
Stability Lobes ◽  
Milling Operations ◽  
The Stability

The aim of this paper is to obtain the stability lobes for milling operations with a nonlinear cutting force model. The work is focused on the generation of stability lobes based on a formulation with Chebyshev polynomials and the semidiscretization method, considering a nonlinear cutting force model. Comparisons were conducted between experimental data at 5% radial immersion with aluminum workpiece and predictions based on Chebyshev and semidiscretization. In all cases, the use of nonlinear cutting force model provides better prediction of process stability conditions.

Chatter in Turning Process Incorporating the Effect of Ploughing Force

1999 ◽  
Author(s):  
Z. C. Wang ◽  
W. L. Cleghorn ◽  
S. D. Yu
Keyword(s):  
Stability Analysis ◽  
Cutting Force ◽  
Force Model ◽  
Turning Process ◽  
Cutting Force Model ◽  
Stability Curve ◽  
Characteristic Roots ◽  
The Laplace Transform ◽  
Machining System ◽  
The Stability

Abstract In this paper, the stability analysis of turning process is performed based on a new cutting force model which includes the effect of ploughing force. This approach utilized the Laplace transform to identify the characteristic roots of the examined machining system. The stability of the machining system can then be determined by examining the locations of the characteristic roots. The stability curve for a specific turning process can then be plotted. The effect of different cutting force models on the stability is also investigated. The results clearly demonstrate some chatter phenomena observed by other researchers.

Stability of Turning Process with a Continuous Delay Model

2012 ◽  
Vol 500 ◽  
pp. 20-25 ◽  
Author(s):  
Qing Hua Song ◽  
Xing Ai ◽  
Bing Guo
Keyword(s):  
Governing Equation ◽  
Distributed Delay ◽  
Space Representation ◽  
Force Model ◽  
Delay Model ◽  
Cutting Force Model ◽  
Third Order ◽  
State Space Representation ◽  
Continuous Delay ◽  
The Stability

An alternative physical explanation for process damping where a distributed cutting force model, along with a function distribution over the tool-chip interface, is assumed, is described. An exponential shape function is used to approximate the force distribution on the tool-chip interface. The distributed force model results in a more complicated governing equation, a second-order delayed integrodifferential equation, which involves both a discrete and distributed delay. An approach to transform and normalize the governing equation of motion into a third-order discrete system is described and the state-space representation of the new system is obtained. The semi-discretization method is then used to chart the stability boundaries for turning operation.

An Improved Tool Path Model Including Periodic Delay for Chatter Prediction in Milling

2006 ◽  
Vol 2 (2) ◽  
pp. 167-179 ◽  
Author(s):  
R. P. H. Faassen ◽  
N. van de Wouw ◽  
H. Nijmeijer ◽  
J. A. J. Oosterling
Keyword(s):  
Periodic Solution ◽  
Cutting Force ◽  
Tool Path ◽  
Chip Thickness ◽  
Milling Process ◽  
Path Model ◽  
Force Model ◽  
Cutting Force Model ◽  
Periodic Delay ◽  
The Stability

The efficiency of the high-speed milling process is often limited by the occurrence of chatter. In order to predict the occurrence of chatter, accurate models are necessary. In most models regarding milling, the cutter is assumed to follow a circular tooth path. However, the real tool path is trochoidal in the ideal case, i.e., without vibrations of the tool. Therefore, models using a circular tool path lead to errors, especially when the cutting angle is close to 0 or π radians. An updated model for the milling process is presented which features a model of the undeformed chip thickness and a time-periodic delay. In combination with this tool path model, a nonlinear cutting force model is used, to include the dependency of the chatter boundary on the feed rate. The stability of the milling system, and hence the occurrence of chatter, is investigated using both the traditional and the trochoidal model by means of the semi-discretization method. Due to the combination of this updated tool path model with a nonlinear cutting force model, the periodic solution of this system, representing a chatter-free process, needs to be computed before the stability can be investigated. This periodic solution is computed using a finite difference method for delay-differential equations. Especially for low immersion cuts, the stability lobes diagram (SLD) using the updated model shows significant differences compared to the SLD using the traditional model. Also the use of the nonlinear cutting force model results in significant differences in the SLD compared to the linear cutting force model.

STABILITY AND HOPF BIFURCATIONS IN A DELAYED PREDATOR–PREY SYSTEM WITH A DISTRIBUTED DELAY

2009 ◽  
Vol 19 (07) ◽  
pp. 2283-2294 ◽  
Author(s):  
CUN-HUA ZHANG ◽  
XIANG-PING YAN
Keyword(s):  
Functional Differential Equations ◽  
Distributed Delay ◽  
Positive Equilibrium ◽  
Hopf Bifurcations ◽  
Normal Form Theory ◽  
Center Manifold Reduction ◽  
Predator Prey ◽  
Prey System ◽  
Functional Differential ◽  
The Stability

This paper is concerned with a delayed Lotka–Volterra two-species predator–prey system with a distributed delay. By linearizing the system at the positive equilibrium and analyzing the associated characteristic equation, the asymptotic stability of positive equilibrium is investigated and Hopf bifurcations are demonstrated. It is found that the positive equilibrium of the system is always locally asymptotically stable when the delay kernel is the weak kernel while there is a stability switch of positive equilibrium when the delay kernel is the strong kernel and the system can undergo a Hopf bifurcation at the positive equilibrium when the average time delay in the delay kernel crosses certain critical values. In particular, by applying the normal form theory and center manifold reduction to functional differential equations (FDEs), the explicit formula determining the direction of Hopf bifurcations and the stability of bifurcated periodic solutions is given. Finally, some numerical simulations are also included to support the analytical results obtained.

scholarly journals Generalized cutting force model for peripheral milling of wood, based on the effect of density, uncut chip cross section, grain orientation and tool helix angle

2021 ◽  
Author(s):  
R. Curti ◽  
B. Marcon ◽  
L. Denaud ◽  
M. Togni ◽  
R. Furferi ◽  
...  
Keyword(s):  
Cutting Force ◽  
Chip Thickness ◽  
Helix Angle ◽  
Force Model ◽  
Cutting Force Model ◽  
Peripheral Milling ◽  
Grain Angle ◽  
Model Based ◽  
Cutting Coefficients ◽  
Machining Operations

AbstractThe influence of the grain angle on the cutting force when milling wood is not yet detailed, apart from particular cases (end-grain, parallel to the grain, or in some rare cases 45°-cut). Thus, setting-up wood machining operations with complex paths still relies mainly on the experience of the operators because of the lack of scientific knowledge easily transferable to the industry. The aim of the present work is to propose an empirical model based on specific cutting coefficients for the assessment of cutting force when peripheral milling of wood based on the following input: uncut chip thickness and width, grain angle (angle between the tool velocity vector and the grain direction of the wood), density and tool helix angle. The specific cutting coefficients were determined by peripheral milling with different depths of cut wood disks issued from different wood species on a dynamometric platform to record the forces. Milling a sample into a round shape (a disk) allows to measure the cutting forces toward every grain angle into a sole basic diameter reduction operation. Force signals are then post-processed to carefully clean the natural vibrations of the system without impacting their magnitudes. The experiment is repeated on five species with a large range of densities, machining two disks per species for five depths of cut in up- and down milling conditions for three different tool helix angles. Finally, a simple cutting force model, based on the previously cited parameters, is proposed, and its robustness analysed.

Modeling Dynamic Stability and Cutting Forces in Micro Milling of Ti6Al4V Using Intermittent Oblique Cutting Finite Element Method Simulation-Based Force Coefficients

2020 ◽  
Vol 142 (9) ◽  
Author(s):  
Priyabrata Sahoo ◽  
Karali Patra ◽  
Vishnu K. Singh ◽  
Rinku K. Mittal ◽  
Ramesh K. Singh
Keyword(s):  
Finite Element Method ◽  
Cutting Force ◽  
Dynamic Stability ◽  
Micro Milling ◽  
Force Model ◽  
Cutting Simulation ◽  
Oblique Cutting ◽  
Force Coefficients ◽  
Stability Model ◽  
The Stability

Abstract Tool breakage is a significant issue in micro milling owing to the less stiffness of the micro tool. To cope up with such limitation, precise predictions of dynamic stability, and cutting force have the utmost importance to monitor and optimize the process. In this article, dynamic stability and cutting force are predicted precisely for micro milling of Ti6Al4V by obtaining force coefficients from a novel 3D intermittent oblique cutting finite element method (FEM) simulation considering the influence of tool run out. First, the stability model is modified by incorporating the appropriate values of limiting angles obtained analytically accounting the trajectories of the flutes due to tool run out. This stability model is utilized to select chatter-free parametric combinations for micro milling tests. Next, an improved cutting force model is developed by incorporating the force coefficients obtained from oblique cutting simulation in the mechanistic model and differentiating the whole machining region into three distinct region considering size effect. The force model also considers the effect of increased edge radius of the worn tool, run out, elastic recovery, ploughing, minimum undeformed chip thickness (MUCT), and limiting angles, cumulatively. The proposed dynamic stability and cutting force models based on the oblique cutting simulation show their adequacy by predicting the stability limit and cutting force more precisely, respectively, as compared to those obtained by orthogonal cutting simulation. Besides, the proposed force model for the worn tool is found to be viable as it is closer to the experimental forces, whereas force model without the incorporation of tool wear underestimated the experimental forces.

scholarly journals Semi-Active Magnetorheological Damper Device for Chatter Mitigation during Milling of Thin-Floor Components

2020 ◽  
Vol 10 (15) ◽  
pp. 5313 ◽  
Author(s):  
Santiago Daniel Puma-Araujo ◽  
Daniel Olvera-Trejo ◽  
Oscar Martínez-Romero ◽  
Gorka Urbikain ◽  
Alex Elías-Zúñiga ◽  
...  
Keyword(s):  
Homotopy Perturbation Method ◽  
Mr Damper ◽  
Magnetorheological Damper ◽  
Force Model ◽  
Cutting Force Model ◽  
Stability Boundaries ◽  
Milling Operations ◽  
Productivity Increase ◽  
Last Stage ◽  
The Stability

The productivity during the machining of thin-floor components is limited due to unstable vibrations, which lead to poor surface quality and part rejection at the last stage of the manufacturing process. In this article, a semi-active magnetorheological damper device is designed in order to suppress chatter conditions during the milling operations of thin-floor components. To validate the performance of the magnetorheological (MR) damper device, a 1 degree of freedom experimental setup was designed to mimic the machining of thin-floor components and then, the stability boundaries were computed using the Enhance Multistage Homotopy Perturbation Method (EMHPM) together with a novel cutting force model in which the bull-nose end mill is discretized in disks. It was found that the predicted EMHPM stability lobes of the cantilever beam closely follow experimental data. The end of the paper shows that the usage of the MR damper device modifies the stability boundaries with a productivity increase by a factor of at least 3.

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