Efficient active chatter mitigation for boring operation by electromagnetic actuator using optimal fractional order PDλ controller
TL;DR: It is observed that a fractional order PDλ controller designed by using combination of pseudo spectral and response optimization techniques is highly efficient in terms of the requirement of low amplitude of the peak force and simplicity of implementation.
Abstract: Due to the factor of limited rigidity of boring bars, small depths of cutting are normally applied for chatter free machining. Stability lobe diagrams can truly represent that limit. However, due to the presence of manufacturing inaccuracies like ovality and eccentricity, these limits are considerably changed. Hence, considering these during modelling the cutting process, stability analysis and controller design is a novel idea, hence implemented in the present work. Dynamic modelling of boring process is presented in detail using a 3-DOF model. Dynamics of such systems is represented using delay differential equations with time periodic coefficients. The system stability is enhanced with active control techniques. The closed loop system considering fractional order PDλ in the loop is a nonlinear time periodic delay differential equation system. Any systematic controller synthesis process for such systems is rarely available in literature. It is observed that a fractional order PDλ controller designed by using combination of pseudo spectral and response optimization techniques is highly efficient in terms of the requirement of low amplitude of the peak force and simplicity of implementation. Transient vibrations can also be quenched in a limited period of time by using this controller. Different control techniques available in literature (H∞ Loop shaping and PD control) are tested and compared to the proposed controller for enhancing the material removal rates and surface finish of the workpiece. By using the active chatter control, the chatter can be efficiently reduced and the material removal rate can be increased. The critical depth of cut is increased from 0.2 mm (open loop) to 0.6 mm (closed loop) with a limited actuator size in the case study.
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TL;DR: In this paper, a magnetorheological (MR) damper is introduced to increase the stability of the boring process, which significantly increases the chatter free depth of cut on the stability lobe diagrams.
Abstract: Chatter is a limiting factor during boring of deep holes with long slender boring bars. In this article, a new magnetorheological (MR) damper is introduced to increase the stability of the boring process. The sponge-type configuration of the damper utilizes a minimal amount of MR fluid in the annulus around the boring bar. The MR fluid layer and the electromagnetic circuit are externally applied to the boring bar, which allows easy installation and adjustability in bar length. A custom made, bidisperse MR fluid is used to eliminate particle sedimentation and enhance the lifetime of the damper. The modal analysis of the boring bar with the new MR damper shows improvements in both the damping and the dynamic stiffness of the system. This enhancement significantly increases the chatter-free depth of cut on the stability lobe diagrams. This article presents the experimental validations on the boring of AL 7075 and Inconel 718 workpieces which are materials widely used in many aerospace applications. The damper is installed on a conventional boring bar for a CNC machining center setup, and its performance is tested under various machining conditions.
6 citations
TL;DR: In this article, the axial ultrasonic vibration-assisted boring (AUVB) method has been used for aviation deep-hole machining and the results demonstrate that AUVB has obvious advantages in reducing boring force, improving boring accuracy, suppressing vibration and promoting surface quality.
Abstract: Deep-holes are typical parts of aircraft structures, which is difficult to be machined. Boring assisted with ultrasonic vibration-assisted cutting has been proved to greatly enhance machining performance, especially for Ti6Al4V aviation alloy. This paper focuses on the machining extra-large aspect ratio (exceeding 20) of Ti6Al4V aviation deep-hole with the axial ultrasonic vibration-assisted boring (AUVB) method. First, the kinetics of the AUVB process is analyzed and a retrospective of its separation cutting feature is provided. Subsequently, a multi-stepped cantilever beam model of boring bar is established to analyze its static rigidity and dynamic stability. The aperture error is deduced, and then size coefficient is put forward to represent the static rigidity of the boring bar, which is inversely proportional to the diameter. In addition, two different vibration cases, namely modal-coupling vibration and regenerative vibration are considered for dynamic stability analysis. Next, the morphology of bored surface is analyzed, and the geometric height of peaks formed by AUVB and CB are calculated. Phase shift φ= π is suggested for obtaining a better surface in AUVB. Finally, the feasibility of AUVB on the machining of extra-large aspect ratio Ti6Al4V titanium alloy aviation deep-hole is verified through systematic experiments. Results demonstrate that AUVB has obvious advantages in reducing boring force, improving boring accuracy, suppressing vibration and promoting surface quality. Furthermore, the aperture error decreases to 50% and vibration amplitudes decrease to only 20–25%. The overall surface roughness of the deep-hole part stays below Ra=0.8μm with rotational speeds of 60r/min and 80r/min, and the surface residual stress state is transferred from the tensile state to a compressive one. As a result, not only AUVB can provide better boring accuracy and surface finish, but it also can enhance the surface fatigue properties.
TL;DR: This paper improves the optimal chatter control through a more accurate modeling method which considers the cutting tool as a cantilever Euler–Bernoulli beam and the TMD as a two degrees of freedom system including translation vibration and rotation vibration of the mass block.
Abstract: The slender cutting tools are employed in many conditions like boring and milling processes, but those machining processes often accompany with chatter phenomenon which will aggravate the machining efficiency and surface quality. The use of tuned mass damper (TMD) to damp slender tools is considered as a practical and effective way for chatter suppression. Generally, the TMD is embedded inside the hollow cutting tool with two spring-damping elements supporting the mass block at both ends. For the convenience of optimization calculation, the damped tool is generally modeled as an oscillation system with two equivalent lumped mass. With this simplified model, the difference of vibration displacements between two spring-damping elements is ignored. This makes it very difficult to tune the TMD to the best according to the optimization result in practical application especially when both cutting tool and TMD have a slender characteristic. This paper improves the optimal chatter control through a more accurate modeling method which considers the cutting tool as a cantilever Euler–Bernoulli beam and the TMD as a two degrees of freedom system including translation vibration and rotation vibration of the mass block. Based on the proposed model, the influences of the position and length of TMD on the optimal design parameters of two spring-damping elements are analyzed through a series of optimization. The results show that there are great differences in the chatter control mechanism of two spring-damping elements and it is very important to choose respective appropriate stiffness and damping parameters for two spring-damping elements in the TMD damped slender cutting tools. Only in this way can the TMD be tuned in practice to the best performance for chatter control of slender cutting tools. Furthermore, based on the simulation results and comparisons with other conventional modeling methods, the difference and superiority of tuning optimization are discussed and the accuracy and practicability of the proposed modeling method are verified with a designed damped end mill cutter and some impact tests.
07 Sep 2021
TL;DR: In this paper, a numerical scheme based on the numerical inversion of Laplace transform and equal width quadrature rule is proposed for solving a significant class of fractional differential equations.
Abstract: This paper introduces an efficient numerical scheme for solving a significant class of fractional differential equations. The major contributions made in this paper apply a direct approach based on a combination of time discretization and the Laplace transform method to transcribe the fractional differential problem under study into a dynamic linear equations system. The resulting problem is then solved by employing the numerical method of the quadrature rule, which is also a well-developed numerical method. The present numerical scheme, which is based on the numerical inversion of Laplace transform and equal-width quadrature rule is robust and efficient. Some numerical experiments are carried out to evaluate the performance and effectiveness of the suggested framework.
References
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Book•
01 Jan 2005
TL;DR: Robust Control Design with MATLAB is for graduate students and practising engineers who want to learn how to deal with robust control design problems without spending a lot of time in researching complex theoretical developments.
Abstract: Robust Control Design with MATLAB (second edition) helps the student to learn how to use well-developed advanced robust control design methods in practical cases. To this end, several realistic control design examples from teaching-laboratory experiments, such as a two-wheeled, self-balancing robot, to complex systems like a flexible-link manipulator are given detailed presentation. All of these exercises are conducted using MATLAB Robust Control Toolbox 3, Control System Toolbox and Simulink. By sharing their experiences in industrial cases with minimum recourse to complicated theories and formulae, the authors convey essential ideas and useful insights into robust industrial control systems design using major H-infinity optimization and related methods allowing readers quickly to move on with their own challenges. The hands-on tutorial style of this text rests on an abundance of examples and features for the second edition: rewritten and simplified presentation of theoretical and methodological material including original coverage of linear matrix inequalities; new Part II forming a tutorial on Robust Control Toolbox 3; fresh design problems including the control of a two-rotor dynamic system; and end-of-chapter exercises. Electronic supplements to the written text that can be downloaded from extras.springer.com/isbn include: M-files developed with MATLAB help in understanding the essence of robust control system design portrayed in text-based examples; MDL-files for simulation of open- and closed-loop systems in Simulink; and a solutions manual available free of charge to those adopting Robust Control Design with MATLAB as a textbook for courses. Robust Control Design with MATLAB is for graduate students and practising engineers who want to learn how to deal with robust control design problems without spending a lot of time in researching complex theoretical developments.
549 citations
TL;DR: In this paper, an updated version of the semi-discretization method is presented for periodic systems with a single discrete time delay, where the delayed term is approximated as a weighted sum of two neighboring discrete delayed state values and the transition matrix over a single period is determined.
Abstract: An updated version of the semi-discretization method is presented for periodic systems with a single discrete time delay. The delayed term is approximated as a weighted sum of two neighbouring discrete delayed state values and the transition matrix over a single period is determined. Stability charts are constructed for the damped and delayed Mathieu equation for different time-period/time-delay ratios. The convergence of the method is investigated by examples. Stability charts are constructed for 1 and 2 degree of freedom milling models. The codes of the algorithm are also attached in the appendix. Copyright © 2004 John Wiley & Sons, Ltd.
492 citations
TL;DR: In this paper, the authors presented a model of the dynamic cutting force process for the three-dimensional or oblique turning operation, which is linked to a tool-workpiece vibration model.
Abstract: This paper presents a model of the dynamic cutting force process for the three-dimensional or oblique turning operation. To obtain dynamic force predictions, the mechanistic force model is linked to a tool–workpiece vibration model. Particular attention was paid to the inclusion of the cross-coupling between radial and axial vibrations in the force model. The inclusion of this cross-coupling facilitates prediction of the unstable–stable chatter phenomenon which usually occurs in certain cases of finish turning due to process non-linearity. The dynamic force model developed was incorporated into a computer program to obtain time-saving chatter predictions. Experimental tests were performed on AISI 4140 steel workpieces to justify the chatter predictions of the dynamic cutting process model in both the finishing and roughing regimes. Experimental results corroborate the unstable–stable chatter predictions of the model for different cases of finish machining. In addition, experimental results also confirmed the accuracy of chatter predictions for various cases of rough turning.
112 citations
TL;DR: In this article, an innovative chatter suppression method based on a magnetorheological (MR) fluid-controlled boring bar for chatter suppression is developed, which changes stiffness and undergoes a phase transformation when subjected to an external magnetic field, is applied to adjust the stiffness of the boring bar and suppress chatter.
Abstract: An innovative chatter suppression method based on a magnetorheological (MR) fluid-controlled boring bar for chatter suppression is developed. The MR fluid, which changes stiffness and undergoes a phase transformation when subjected to an external magnetic field, is applied to adjust the stiffness of the boring bar and suppress chatter. The stiffness and energy dissipation properties of the MR fluid-controlled boring bar can be adjusted by varying the strength of the applied magnetic field. A dynamic model of a MR fluid-controlled boring bar is established based on an Euler–Bernoulli beam model. The stability of the MR fluid-controlled boring system is analyzed, and the simulation results show that regenerative chatter can be suppressed effectively by adjusting the natural frequency of the system. Experiments in different spindle speeds utilizing a MR fluid-controlled boring bar are conducted. Under a 1 Hz square wave current, chatter can be suppressed, as evidenced by the elimination of chatter marks on the machined surfaces and the reduction in the vibration acceleration at the tip of the boring bar.
102 citations
TL;DR: In this article, the use of an active dynamic absorber to suppress machine tool chatter in a boring bar is studied, where the vibrations of the system are reduced by moving an absorber mass using an active device such as an piezoelectric actuator, to generate an inertial force that counteracts the disturbance acting on the main system.
Abstract: In this paper, the use of an active dynamic absorber to suppress machine tool chatter in a boring bar is studied. The vibrations of the system are reduced by moving an absorber mass using an active device such as an piezoelectric actuator, to generate an inertial force that counteracts the disturbance acting on the main system. An equivalent lumped mass model of a boring bar with active dynamic absorber is considered. A cutting process model that considers the dynamic variation of shear and friction angle, that causes self-excited chatter during the cutting process, is applied to the lumped mass model. The theory of regenerative chatter is also applied to the model. Stability boundaries have been calculated for maximum permissible width of cut as a function of cutting speed. A comparison of the boundaries for chatter-free cutting operation of a plain boring bar, a boring bar with passive tuned dynamic absorber and a boring bar with active dynamic absorber is provided in this paper. The comparison shows that a substantial increase in the maximum permissible width of cut for stable cutting operation, over a range of cutting speeds, is obtained for a boring bar equipped with an active dynamic absorber.
100 citations
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