Robust Active Chatter Control in Milling Processes With Variable Pitch Cutters

2018 ◽  
Vol 140 (10) ◽  
Author(s):  
Tao Huang ◽  
Lijun Zhu ◽  
Shengli Du ◽  
Zhiyong Chen ◽  
Han Ding
Keyword(s):  
Nonlinear Differential Equations ◽  
Magnetic Bearing ◽  
Active Magnetic Bearing ◽  
Linear Matrix ◽  
Variable Pitch ◽  
Stability Lobe ◽  
Milling Operations ◽  
Controller Gain ◽  
Chatter Control ◽  
The Stability

Milling chatters caused by the regenerative effect is one of the major limitations in increasing the machining efficiency and accuracy of milling operations. This paper studies robust active chatter control for milling processes with variable pitch cutters whose dynamics are governed by multidelay nonlinear differential equations. We propose a state feedback controller based on linear matrix inequality (LMI) approach that can enlarge multiple stability domains in the stability lobe diagram (SLD) while the controller gain is minimized. Numerical simulations of active magnetic bearing systems demonstrate the effectiveness of the proposed method.

Nonlinear Oscillation of a Rotor-AMB System With Time Varying Stiffness and Multi-External Excitations

2009 ◽  
Vol 131 (3) ◽  
Author(s):  
M. Kamel ◽  
H. S. Bauomy
Keyword(s):  
Steady State ◽  
Order Approximation ◽  
Nonlinear Differential Equations ◽  
Steady State Solution ◽  
Magnetic Bearing ◽  
Active Magnetic Bearing ◽  
Multiple Time ◽  
Time Varying ◽  
The Stability ◽  
Amb System

The rotor-active magnetic bearing system subjected to a periodically time-varying stiffness having quadratic and cubic nonlinearities is studied and solved. The multiple time scale technique is applied to solve the nonlinear differential equations governing the system up to the second order approximation. All possible resonance cases are deduced at this approximation and some of them are confirmed by applying the Rung–Kutta method. The main attention is focused on the stability of the steady-state solution near the simultaneous principal resonance and the effects of different parameters on the steady-state response. A comparison is made with the available published work.

An Evaluation of Stability Indices Using Sensitivity Functions for Active Magnetic Bearing Supported High-Speed Rotor

2006 ◽  
Vol 129 (2) ◽  
pp. 230-238 ◽  
Author(s):  
Naohiko Takahashi ◽  
Hiroyuki Fujiwara ◽  
Osami Matsushita ◽  
Makoto Ito ◽  
Yasuo Fukushima
Keyword(s):  
High Speed ◽  
Transfer Functions ◽  
Mimo System ◽  
Magnetic Bearing ◽  
Singular Value ◽  
Active Magnetic Bearing ◽  
Sensitivity Functions ◽  
Phase Lags ◽  
The Stability ◽  
Stability Indices

In active magnetic bearing (AMB) systems, stability is the most important factor for reliable operation. Rotor positions in radial direction are regulated by four-axis control in AMB, i.e., a radial system is to be treated as a multi-input multioutput (MIMO) system. One of the general indices representing the stability of a MIMO system is “maximum singular value” of a sensitivity function matrix, which needs full matrix elements for calculation. On the other hand, ISO 14839-3 employs “maximum gain” of the diagonal elements. In this concept, each control axis is considered as an independent single-input single-output (SISO) system and thus the stability indices can be determined with just four sensitivity functions. This paper discusses the stability indices using sensitivity functions as SISO systems with parallel/conical mode treatment and/or side-by-side treatment, and as a MIMO system with using maximum singular value; the paper also highlights the differences among these approaches. In addition, a conversion from usual x∕y axis form to forward/backward form is proposed, and the stability is evaluated in its converted form. For experimental demonstration, a test rig diverted from a high-speed compressor was used. The transfer functions were measured by exciting the control circuits with swept signals at rotor standstill and at its 30,000 revolutions/min rotational speed. For stability limit evaluation, the control loop gains were increased in one case, and in another case phase lags were inserted in the controller to lead the system close to unstable intentionally. In this experiment, the side-by-side assessment, which conforms to the ISO standard, indicates the least sensitive results, but the difference from the other assessments are not so great as to lead to inadequate evaluations. Converting the transfer functions to the forward/backward form decouples the mixed peaks due to gyroscopic effect in bode plot at rotation and gives much closer assessment to maximum singular value assessment. If large phase lags are inserted into the controller, the second bending mode is destabilized, but the sensitivity functions do not catch this instability. The ISO standard can be used practically in determining the stability of the AMB system, nevertheless it must be borne in mind that the sensitivity functions do not always highlight the instability in bending modes.

Harmonic disturbance attenuation in a three-pole active magnetic bearing test rig using a modified notch filter

2016 ◽  
Vol 23 (5) ◽  
pp. 770-781 ◽  
Author(s):  
S Mahdi Darbandi ◽  
Mehdi Behzad ◽  
Hassan Salarieh ◽  
Hamid Mehdigholi
Keyword(s):  
Notch Filter ◽  
Magnetic Bearing ◽  
Active Magnetic Bearing ◽  
Disturbance Attenuation ◽  
Test Rig ◽  
Stability Margins ◽  
Periodic Disturbances ◽  
Mass Unbalance ◽  
Gain Margin ◽  
The Stability

This study is concerned with the problem of harmonic disturbance rejection in active magnetic bearing systems. A modified notch filter is presented to identify both constant and harmonic disturbances caused by sensor runout and mass unbalance. The proposed method can attenuate harmonic displacement and currents at the synchronous frequency and its integer multiples. The reduction of stability is a common problem in adaptive techniques because they alter the original closed-loop system. The main advantage of the proposed method is that it is possible to determine the stability margins of the system by few parameters. The negative phase shift of the modified notch filter can be tuned to achieve a desired phase margin, while the gain margin can also be adjusted separately. It is shown that the modified notch filter can be designed to suppress multiple harmonics at the same time. It is implemented on a three-pole magnetic bearing test rig to evaluate its performance. Simulation and experimental results indicate that the presented method can be successfully applied to compensate the periodic disturbances such as sensor runout and mass unbalance in active magnetic bearing systems.

A Numerical Study on Effect of Electromagnetic Actuator on Rigid Rotor Supported on Gas Foil Bearing

2017 ◽  
Author(s):  
Kamal Kumar Basumatary ◽  
Gaurav Kumar ◽  
Karuna Kalita ◽  
Sashindra Kumar Kakoty
Keyword(s):  
Numerical Study ◽  
Load Capacity ◽  
Current Trend ◽  
Magnetic Bearing ◽  
Active Magnetic Bearing ◽  
Normal Operation ◽  
Electromagnetic Actuator ◽  
Rigid Rotor ◽  
Magnetic Actuator ◽  
The Stability

Generally, Gas Foil Bearings (GFBs) are used in high speed machineries which are quite prone to instability or wear and tear. The current trend is to develop hybrid bearings which has conventional bearing (GFB) along with active magnetic bearing as an electromagnetic actuator (EMA). The GFBs are used for normal operation and the magnetic actuator can be used for the improvement of the stability and the load capacity of the bearing. In the present work a numerical study has been carried out to study the effects of magnetic actuator on the stability of bump type GFB supported rigid rotor. A rigid rotor supported on two identical GFBs with and without EMA has been investigated. The electromagnetic forces are incorporated in the equation of motion to provide the active control. A PD controller has been used as a controller for the magnetic actuator. It has been observed that the incorporation of EMA to the GFB reduces the sub synchronous vibrations and hence increases the stability.

Nonlinear Dynamics of a Magnetically Supported Rotor on Safety Auxiliary Bearings

1998 ◽  
Vol 120 (2) ◽  
pp. 596-606 ◽  
Author(s):  
X. Wang ◽  
S. Noah
Keyword(s):  
Steady State ◽  
Periodic Solutions ◽  
Nonlinear Dynamic System ◽  
Magnetic Bearing ◽  
Active Magnetic Bearing ◽  
Fixed Point Algorithm ◽  
Friction Forces ◽  
Flexible Supports ◽  
Multiple Periodic Solutions ◽  
The Stability

This study concerns the dynamic response of a rotor landed on auxiliary (catcher) bearings in an Active Magnetic Bearing (AMB) supported rotor, following postulated loss of power or overload of the AMB. An analytical model involving a disk, a shaft and auxiliary bearings on damped flexible supports is constructed and appropriate equations of the nonlinear dynamic system are developed. The equations include a switch function to indicate contact/non-contact events and determine the existence of contact normal forces and tangential friction forces between the shaft and the bearings. Steady state solutions are obtained. An analytical method was formulated and used to yield solutions for cases with well balanced rotors, in absence of any side forces. The Fixed Point Algorithm (FPA) is used to obtain steady state periodic solutions of the unbalanced rotor for various parameters. The FPA is used to determine the stability of the periodic solutions and the type of bifurcation involved. Multiple periodic solutions, quasi-periodic and chaotic responses are detected and discussed. A set of preliminary guidelines for selection of the parameters of the catcher bearings is given.

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.

An FPGA Implementation of the Robust Controller for the Active Magnetic Bearing System

2009 ◽  
Vol 147-149 ◽  
pp. 399-409
Author(s):  
Zbigniew Kulesza ◽  
Zdzisław Gosiewski
Keyword(s):  
Dynamic Properties ◽  
Dynamic Performance ◽  
Magnetic Bearing ◽  
Design Flow ◽  
Active Magnetic Bearing ◽  
Project Design ◽  
Robust Controller ◽  
Fpga Chip ◽  
The Stability ◽  
Bearing System

The article presents the project design flow that leads to the implementation of the robust controller law in the FPGA chip. The designed robust FPGA controller is going to be used in the heteropolar active magnetic bearing system. The hardware and software architectures of the designed controller are presented. The hardware consists of the market available Spartan-3 Development Board and two specially designed A/D and D/A converters boards. The software architecture is made of several VHDL entities that are translated into the target FPGA chip. The results of the experimental preliminary tests show that the dynamic properties of the designed controller are very good and the authors hope that the dynamic performance, especially the stability of the whole active magnetic bearing system, will improve.

Effect of Thrust Magnetic Bearing on Stability and Bifurcation of a Flexible Rotor Active Magnetic Bearing System

2003 ◽  
Vol 125 (3) ◽  
pp. 307-316 ◽  
Author(s):  
Y. S. Ho ◽  
H. Liu ◽  
L. Yu
Keyword(s):  
Periodic Motion ◽  
Magnetic Bearing ◽  
Rotor System ◽  
Magnetic Bearings ◽  
Active Magnetic Bearing ◽  
Flexible Rotor ◽  
Periodic Motions ◽  
Stability And Bifurcation ◽  
Mass Eccentricity ◽  
The Stability

This paper is concerned with the effect of a thrust active magnetic bearing (TAMB) on the stability and bifurcation of an active magnetic bearing rotor system (AMBRS). The shaft is flexible and modeled by using the finite element method that can take the effects of inertia and shear into consideration. The model is reduced by a component mode synthesis method, which can conveniently account for nonlinear magnetic forces and moments of the bearing. Then the system equations are obtained by combining the equations of the reduced mechanical system and the equations of the decentralized PID controllers. This study focuses on the influence of nonlinearities on the stability and bifurcation of T periodic motion of the AMBRS subjected to the influences of both journal and thrust active magnetic bearings and mass eccentricity simultaneously. In the stability analysis, only periodic motion is investigated. The periodic motions and their stability margins are obtained by using shooting method and path-following technique. The local stability and bifurcation behaviors of periodic motions are obtained by using Floquet theory. The results indicate that the TAMB and mass eccentricity have great influence on nonlinear stability and bifurcation of the T periodic motion of system, cause the spillover of system nonlinear dynamics and degradation of stability and bifurcation of T periodic motion. Therefore, sufficient attention should be paid to these factors in the analysis and design of a flexible rotor system equipped with both journal and thrust magnetic bearings in order to ensure system reliability.

scholarly journals The Stability of Magnetic Levitation Milling System Based on Modal Decoupling Control

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Xiaoli Qiao ◽  
Xiaoping Tang
Keyword(s):  
High Speed ◽  
Stability Region ◽  
Magnetic Levitation ◽  
Coupling Effect ◽  
Magnetic Bearing ◽  
Decoupling Control ◽  
Active Magnetic Bearing ◽  
High Speed Milling ◽  
Milling Stability ◽  
The Stability

Milling stability not only reduces the surface quality of the workpiece but also seriously restricts the high-speed development of CNC machine tools. The electric spindle rotor system with the active magnetic bearing has a strong gyro coupling effect, and with the increasing rotor speed, it will become a major unfavorable factor for the stability of the system during high-speed milling. The strong gyro coupling effect makes the stability region narrow at the time of high-speed milling. So, a modal decoupling control method that can reduce the effects of the gyro effect on the magnetic levitation milling system under high-speed milling is proposed. The effects of the gyro coupling of the magnetic bearing rotor on the milling stability region before and after the decoupling control are studied, which show that the modal decoupling control technology can reduce the effects of the gyro effect on the magnetic levitation milling system.

scholarly journals Vibration Torque Suppression for Magnetically Suspended Flywheel Using Improved Synchronous Rotating Frame Transformation

2019 ◽  
Vol 2019 ◽  
pp. 1-13 ◽  
Author(s):  
Cong Peng ◽  
Kaiwen Cai ◽  
Zhiquan Deng ◽  
Kexiang Li
Keyword(s):  
Control Method ◽  
Magnetic Bearing ◽  
Active Magnetic Bearing ◽  
Rotating Frame ◽  
Overall Stability ◽  
High Power Consumption ◽  
Frame Transformation ◽  
The Stability ◽  
Amb System ◽  
Gyroscopic Effects

Synchronous vibration, a common issue in active magnetic bearing (AMB) system, is mainly caused by mass imbalance of the rotor. It comes with high-power consumption and serious impact on the housing base, dramatically degrading the performance of AMB. Magnetically suspended flywheel (MSFW), which owns a flat rotor and consequently shows strong gyroscopic effects even at low operating speed, requires additional attention not only for suppressing the synchronous vibration but also for maintaining the overall stability faced with the coupled dynamics. In this work, in order to suppress the vibration torques in MSFW with significant gyroscopic effects, an improved synchronous rotating frame- (SRF-) based control method is proposed. The proposed method introduces the compensation phase for stability adjustment and aims at simultaneously suppressing the synchronous components in the coupled axes. Firstly, the vibration torque model of MSFW is established, and the baseline control strategy for suspension and gyroscopic effects restrain is derived. Then, the principle and implementation of the improved SRF-based vibration torque method are analyzed, which aims at suppressing the synchronous vibration torques through attenuating synchronous components in coil currents. Moreover, the stability of the overall closed-loop system is analyzed. Finally, the effectiveness of the proposed method is verified through simulation and experimental results.

Sign in / Sign up

Export Citation Format

Share Document