Closed-form estimations of the bistable region in metal cutting via the method of averaging

Molnár, Tamás G.; Insperger, Tamás; Stépàn, Gábor

doi:10.1016/j.ijnonlinmec.2018.09.005

Cited by 15 publications

(10 citation statements)

References 43 publications

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“…In practice, end-cutting edge and back-cutting phenomenon introduce additional cutting forces [11], although attempts have been made to develop mechanistic model to predict cutting force from basic principles considering mechanical properties of materials and established principles of metal cutting. Micromilling is characterized by multifactor feature and uncertainty; the cutting forces produced by the machining process contain synthetic feature, such as linear and nonlinear characteristics [25,32], while a single prediction model is unable to capture multiple data features at the same time leading to unsatisfactory prediction precision. The modified models combine the mechanistic model with Gaussian process adjustment model; on the one hand, the mechanistic model is used to control the global trend; on the other hand, the Gaussian process regression (GPR) algorithm is suitable for nonlinearity capturing and location adjustment to reduce the deviation between the experimental and the predicted values [33].…”

Section: Predicting Performance Evaluationmentioning

confidence: 99%

“…Gaussian process models can flexibly represent the complex nonlinear relationships without presuppose model and are the common approaches that are used to local adjustment in the method which composes the simulation data with different levels of accuracy to improve the prediction accuracy [24]. Micro-end-milling is a complicated process, and cutting force during micro-end-milling process has nonlinearity characteristics [25]. The mechanistic model of cutting force cannot fully express the relationship between parameters and cutting force.…”

Section: Introductionmentioning

confidence: 99%

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Modified Mechanistic Model Based on Gaussian Process Adjusting Technique for Cutting Force Prediction in Micro‐End Milling

Liao

Zhang

Chen

et al. 2019

Mathematical Problems in Engineering

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Micro-end milling is in common use of machining micro- and mesoscale products and is superior to other micro-machining processes in the manufacture of complex structures. Cutting force is the most direct factor reflecting the processing state, the change of which is related to the workpiece surface quality, tool wear and machine vibration, and so on, which indicates that it is important to analyze and predict cutting forces during machining process. In such problems, mechanistic models are frequently used for predicting machining forces and studying the effects of various process variables. However, these mechanistic models are derived based on various engineering assumptions and approximations (such as the slip-line field theory). As a result, the mechanistic models are generally less accurate. To accurately predict cutting forces, the paper proposes two modified mechanistic models, modified mechanistic models I and II. The modified mechanistic models are the integration of mathematical model based on Gaussian process (GP) adjustment model and mechanical model. Two different models have been validated on micro-end-milling experimental measurement. The mean absolute percentage errors of models I and II are 7.76% and 6.73%, respectively, while the original mechanistic model’s is 15.14%. It is obvious that the modified models are in better agreement with experiment. And model II performs better between the two modified mechanistic models.

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Section: Predicting Performance Evaluationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Modified Mechanistic Model Based on Gaussian Process Adjusting Technique for Cutting Force Prediction in Micro‐End Milling

Liao

Zhang

Chen

et al. 2019

Mathematical Problems in Engineering

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show abstract

“…( 38) at the Hopf bifurcation points. The normal forms near the Hopf bifurcation can be obtained using the MMS [27] or the method of averaging [44,45] or center manifold reduction [46]. These normal forms can be used to study the stability of the limit cycles born out of Hopf bifurcation.…”

Section: Hopf Bifurcationmentioning

confidence: 99%

Supercritical and Subcritical Hopf Bifurcations in a Delay Differential Equation Model of a Heat-Exchanger Tube Under Cross-Flow

Vourganti

Kandala

Meesala

et al. 2019

Journal of Computational and Nonlinear Dynamics

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Nonlinear vibrations of a heat-exchanger tube modeled as a simply supported Euler–Bernoulli beam under axial load and cross-flow have been studied. The compressive axial loads are a consequence of thermal expansion, and tensile axial loads can be induced by design (prestress). The fluid forces are represented using an added mass, damping, and a time-delayed displacement term. Due to the presence of the time-delayed term, the equation governing the dynamics of the tube becomes a partial delay differential equation (PDDE). Using the modal-expansion procedure, the PDDE is converted into a nonlinear delay differential equation (DDE). The fixed points (zero and buckled equilibria) of the nonlinear DDE are found, and their linear stability is analyzed. It is found that stability can be lost via either supercritical or subcritical Hopf bifurcation. Using Galerkin approximations, the characteristic roots (spectrum) of the DDE are found and reported in the parametric space of fluid velocity and axial load. Furthermore, the stability chart obtained from the Galerkin approximations is compared with the critical curves obtained from analytical calculations. Next, the method of multiple scales (MMS) is used to derive the normal-form equations near the supercritical and subcritical Hopf bifurcation points for both zero and buckled equilibrium configurations. The steady-state amplitude response equation, obtained from the MMS, at Hopf bifurcation points is compared with the numerical solution. The coexistence of multiple limit cycles in the parametric space is found, and has implications in the fatigue life calculations of the heat-exchanger tubes.

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“…It is important to highlight commonly used methods to overcome challenges related to the computational requirement for solving nonlinear dynamic models and high signal-to-noise ratio demand for data processing [20]. The equations of motion can be solved algebraically using techniques such as the harmonic balance method (HBM) [50], incremental HBM [51], method of averaging [52], Volterra series [53], normal form [54], nonlinear normal modes [55], or multiple scales [56,57]. In this study, HBM was applied to analytically solve the equation of motion, where the results were in good agreement with the numerical solution.…”

Section: Introductionmentioning

confidence: 99%

Highly Sensitive Nonlinear Identification to Track Early Fatigue Signs in Flexible Structures

Habtour

Maio

Masmeijer

et al. 2021

Journal of Nondestructive Evaluation, Diagnostics and Prognostics of Engineering Systems

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This study describes a physics-based and data-driven nonlinear system identification approach for detecting early fatigue damage due to vibratory loads. The approach also allows for tracking the evolution of damage in real-time. Nonlinear parameters such as geometric stiffness, cubic damping and phase angle shift can be estimated as a function of fatigue cycles, which are demonstrated experimentally using flexible aluminum 7075-T6 structures exposed to vibration. Nonlinear system identification is utilized to create and update nonlinear frequency response functions, backbone curves and phase traces to visualize and estimate the structural health. Findings show that the dynamic phase is more sensitive to the evolution of early fatigue damage than nonlinear parameters such as the geometric stiffness and cubic damping parameters. A modifed Carrella-Ewins method is introduced to calculate the backbone from the nonlinear signal response, which is in good agreement with the numerical and harmonic balance results. The phase tracing method is presented, which appears to detect damage after approximately 40% of fatigue life, while the geometric stiffness and cubic damping parameters are capable of detecting fatigue damage after approximately 50% of the life-cycle.

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Closed-form estimations of the bistable region in metal cutting via the method of averaging

Cited by 15 publications

References 43 publications

Modified Mechanistic Model Based on Gaussian Process Adjusting Technique for Cutting Force Prediction in Micro‐End Milling

Modified Mechanistic Model Based on Gaussian Process Adjusting Technique for Cutting Force Prediction in Micro‐End Milling

Supercritical and Subcritical Hopf Bifurcations in a Delay Differential Equation Model of a Heat-Exchanger Tube Under Cross-Flow

Highly Sensitive Nonlinear Identification to Track Early Fatigue Signs in Flexible Structures

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