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.

Effect of Progressive Tool Wear on the Evolution of the Dynamic Stability Limits in High-Speed Micromilling of Ti-6Al-4V

2019 ◽  
Vol 141 (11) ◽  
Author(s):  
Rinku Mittal ◽  
Chinmay Maheshwari ◽  
Salil S. Kulkarni ◽  
Ramesh Singh
Keyword(s):  
Tool Wear ◽  
High Speed ◽  
Domain Model ◽  
Flexural Stiffness ◽  
Wide Range ◽  
Micro Tool ◽  
Complex Features ◽  
The Stability ◽  
Stability Limits ◽  
Micro Tools

Abstract Micromilling can fabricate complex features in a wide range of engineering materials with an excellent finish but the limited flexural stiffness of the micro-end mill can result in catastrophic tool failure. This issue can be overcome by using high rotational speeds. Note that the combination of high rotational speeds and low flexural stiffness can induce process instability which is aggravated by the accelerated wear of the micro-tools at high speeds, specifically, for Ti-alloys. The effect of progressive tool wear on the stability has been investigated in micromilling of Ti-6Al-4V. For incorporating tool wear, the cutting force coefficients are modeled as a function of initial and instantaneous cutting edge radius (CER) and feed per tooth. The initial CER of the micro-tool is considered due to the inherent variability in the tool grinding process. A significant increase (85–114%) in the instantaneous CER is observed with an increase in the length of cut. A 2DOF time-domain model based on semi-discretization method has been used to characterize the evolution of stability limits with an increase in the length of cut. The progressive tool wear affects the stability limits along with the initial CER and the feed per tooth. At higher speeds (90,000–110,000 rpm), the effect of progressive tool wear is pronounced and the stability limits reduce by ∼30% in that range.

Study on Gyroscopic Effect of Magnetic Flywheel Rotor

2011 ◽  
Vol 130-134 ◽  
pp. 970-975
Author(s):  
Xiang Long Wen ◽  
Cao Cao
Keyword(s):  
Feedback Control ◽  
High Speed ◽  
System Stability ◽  
Rotor Speed ◽  
Gyroscopic Effect ◽  
Pd Control ◽  
The Stability ◽  
Gyroscopic Effects ◽  
Zero Points ◽  
Flywheel Rotor

In the high-speed, gyroscopic effects of the flywheel rotor greatly influence the rotor stability. The pole-zero points move to right of s-plane and the damping terms of the pole points become smaller. The stability of the system will get worse with the increasing of rotor speed when the traditional decentralized PD controller is used only. In the paper, a cross-feedback control with decentralized PD control is used for compensating gyroscopic effect. The simulation results show that the system stability is better using the cross-feedback control with decentralized PD control than using the traditional decentralized PD control.

Criteria for the Stability Limit Prediction of High Speed Centrifugal Compressors With Vaneless Diffuser: Part I — Flow Structure Analysis

2020 ◽  
Author(s):  
Carlo Cravero ◽  
Davide Marsano
Keyword(s):  
Rotational Speed ◽  
High Speed ◽  
Stability Limit ◽  
Vaneless Diffuser ◽  
Centrifugal Compressors ◽  
Vaned Diffuser ◽  
High Rotational Speed ◽  
Lower Accuracy ◽  
The Stability ◽  
Computational Resources

Abstract High-speed centrifugal compressor requirements include a wide operating range between choking and stall especially for turbocharging applications. The prediction of the stability limit at different speeds is still challenging. In literature, several studies have been published on the phenomena that trigger the compressor instability. However, a comprehensive analysis of criteria that can be used in the first steps of centrifugal compressors design to predict the stability limit is still missing. In previous work the authors have already presented a criterion, so called “Stability Parameter”, to predict the surge line of centrifugal compressors based on a simplified CFD approach that does not require excessive computational resources and that can be efficiently used in the preliminary design phases. The above methodology has demonstrated its accuracy for centrifugal compressors with vaned diffuser, but a lower accuracy has been detected for vaneless diffusers. Before proceeding to identify additional criteria focused on compressors with vaneless diffuser, an in-depth fluid dynamics analysis has been necessary. This analysis has been also carried out through fully 3D unsteady simulations to allow identifying the real phenomena linked to the trigger of the instability of centrifugal compressors. It has been found how these phenomena are strongly related to the rotational speed, in particular have been shown the key role of the volute at high rotational speed.

scholarly journals Simulation analysis of efficiency and stability for vehicle’s ABS control on combined steering and braking maneuvers

2019 ◽  
Vol 272 ◽  
pp. 01024 ◽  
Author(s):  
Feng YU ◽  
Jun XIE
Keyword(s):  
High Speed ◽  
Control Algorithm ◽  
Degrees Of Freedom ◽  
Simulation Analysis ◽  
Stability Control ◽  
Vehicle Stability ◽  
Slip Ratio ◽  
Braking Performance ◽  
Braking System ◽  
The Stability

Eight degrees of freedom vehicle model was established. Using the method of fuzzy control, the ABS control algorithm was designed based on slip ratio. Simulation analysis was done at speed of 15m/s, 20m/s, 25m/s under turning braking. The results show that the vehicle braking performance and vehicle stability at middle or low speed was improved by using the ABS controller, but qualitative analysis shows that phenomenon of vehicle instability was appeared at high-speed conditions. The turning braking stability under ABS controller was judged quantificationally by the stability judging formula. The results show that the requirements of stability control could not meet with only Anti-lock Braking System.

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.

On the High-Speed Porpoising Instability of a Prismatic Hull

1984 ◽  
Vol 28 (02) ◽  
pp. 77-89 ◽  
Author(s):  
Peter R. Payne
Keyword(s):  
Skin Friction ◽  
High Speed ◽  
Degrees Of Freedom ◽  
Transient Solution ◽  
Delta Wings ◽  
Closed Form Solutions ◽  
Wetted Area ◽  
The Stability ◽  
Transient Forces ◽  
Vertical Impact

Simple closed-form solutions are obtained for the steady-state and transient forces and moments on a prismatic hull at speeds high enough for hydrostatic forces to be negligible and the chines to be above the undisturbed water surface ("chines dry"). We first show that this solution can be transformed to get the correct results for other hydrodynamic problems, such as the vertical impact of a wedge, a slender foil, or the two-dimensional planing of a flat plate. We then show that the full transient solution is essentially identical with Ribner's [1]2 equations for delta wings, except for terms which depend on the reduction in wetted width with heave. These results are employed to study the stability of such a hull on the assumption that only heave and pitch degrees of freedom are important, following the reasoning of Per̂ing [2]. In contradistinction to all four previous studies [2–5], the effect of skin friction is included and is found to be very powerful. If the center of gravity is above the centroid of the wetted area (which it generally is), then the effect of skin friction is stabilizing.

Stability of Flexible Rotors With a LeBlanc Balancer

2011 ◽  
Author(s):  
Leonardo Urbiola-Soto ◽  
Marcelo Lopez-Parra
Keyword(s):  
High Speed ◽  
Particle Image ◽  
Flexible Rotor ◽  
Rotating System ◽  
Stability Behavior ◽  
Piv Technique ◽  
Flexible Rotors ◽  
Image Velocimetry ◽  
The Stability ◽  
Stability Limits

Although the liquid balancer has nearly a century of having been introduced by LeBlanc, little information is available on the dynamic response and stability behavior of this kind of device. Earlier author’s research using a high-speed camera and a Particle Image Velocimetry (PIV) technique showed the existence of a fluid backward traveling wave inside the balancer cavity. This damping phenomenon helps enhance the unbalance response of the rotating system and also raises the stability limits. This paper shows that a flexible rotor employing a LeBlanc balancer has remarkable increase in the threshold speed of instability for aerodynamic cross-coupling and viscous internal friction damping.

Normal Mode Uncoupling of Systems with Time Varying Stiffness

1980 ◽  
Vol 102 (2) ◽  
pp. 379-383 ◽  
Author(s):  
M. Benton ◽  
A. Seireg
Keyword(s):  
Approximate Method ◽  
Normal Mode ◽  
High Speed ◽  
Degrees Of Freedom ◽  
Necessary Conditions ◽  
Coupled Systems ◽  
Time Varying ◽  
Parametric Vibrations ◽  
Gear Trains ◽  
The Stability

This paper investigates the conditions for transforming coupled systems with time-varying stiffness to normal mode coordinates. The stability regions are determined from the normal mode equations and the effect of model damping on the width of these regions is investigated. An approximate method for uncoupling is also presented which can be used to give good practical solutions in situations where the theoretical necessary conditions are not met. The proposed method can provide a simple and effective tool for the analysis of parametric vibrations for systems with any number of degrees of freedom as in the case of high speed gear trains.

Study of the LQR Controller for Magnetic Flywheel Rotor System

2012 ◽  
Vol 150 ◽  
pp. 221-226 ◽  
Author(s):  
Xiang Long Wen ◽  
Chun Sheng Song ◽  
Cao Cao ◽  
Guo Ping Ding
Keyword(s):  
High Speed ◽  
Control Method ◽  
Linear Quadratic Regulator ◽  
Rotor System ◽  
Linear Quadratic ◽  
Gyroscopic Effect ◽  
Lqr Controller ◽  
The Stability ◽  
Gyroscopic Effects ◽  
Flywheel Rotor

Gyroscopic effects in the flywheel rotor greatly influence rotor stability especially at high speed. When the pole-zero position moves to right of s-plane, the damping of the pole is getting smaller, and the stability of system is getting worse with the increasing of rotor speed when the decentralized PD control law is used only. The LQR (linear quadratic regulator) control method is used to reduce gyroscopic effect and forced vibration. The simulation results show that LQR controller have a good performance on the reduction of gyroscopic effect and vibration of magnetic flywheel rotor system.

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