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A dynamical modeling of spindle with Active Magnetic Bearing (AMB) is presented. All the required parameters are included in the model for stability analysis. The original map of stability is generated by Time Domain Simulation. The major importance of forced vibrations is highlighted for a spindle with AMB. Milling test are used to quickly evaluat...
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This study represents the transverse vibrations of an axially accelerating Euler–Bernoulli beam resting on multiple simple supports. This is one of the examples of a system experiencing Coriolis acceleration component that renders such systems gyroscopic. A small harmonic variation with a constant mean value for the axial velocity is assumed in the...
Citations
... In some applications, the rotors are considered to be flexible such as in Refs. [2,27]. Actually, the electromagnet parts are composed of laminations so as to reduce eddy currents within the ferromagnetic material. ...
In machining process, chatter is an unstable dynamic phenomenon which causes overcut and quick tool wear, etc. To avoid chatter, traditional methods aim to optimize machining parameters. But they have inherent disadvantage in gaining highly efficient machining. Active magnetic bearing (AMB) is a promising technology for machining on account of low wear and friction, low maintenance cost, and long operating life. The control currents applied to AMBs allow not only to stabilize the supported spindle but also to actively suppress chatter in milling process. This paper, for the first time, studies an integrated control scheme for stability of milling process with a spindle supported by AMBs. First, to eliminate the vibration of an unloaded spindle rotor during acceleration/deceleration, we present an optimal controller with proper compensation for speed variation. Next, the controller is further enhanced by adding an adaptive algorithm based on Fourier series analysis to actively suppress chatter in milling process. Finally, numerical simulations show that the stability lobe diagram (SLD) boundary can be significantly expanded. Also, a practical issue of constraints on controller output is discussed.
... In some applications, the rotors are considered to be flexible such as in[2,26]. Actually, the electromagnet parts are composed of laminations so as to reduce eddy currents within the ferromagnetic material. ...
Chatter is an undesirable dynamic phenomenon in machining processes, which causes cutting disturbance, overcut, quick tool wear, etc., and thus seriously impairs workpiece quality. To mitigate chatter, traditional methods called passive control focus on optimizing working spindle speeds and depths of cut. But they have inherent disadvantages in gaining highly efficient machining. On the contrary, the research in this paper is along the line of active control. Specifically, an adaptive algorithm is developed based on Fourier series analysis to deal with the so-called regenerative cutting force which causes chatter. As a result, chatter is remarkably mitigated. The performance improvement is illustrated by numerical simulation in terms of both stability lobes diagram (SLD) and surface location error (SLE).
... Since this work, many researchers have improved the knowledge by the stability lobe representation, see e.g. [2,3,4,5]. The behavior of a cutting tool on a lathe has also been studied using the method of multiple scales [6]. ...
This paper presents the interest of an original absorber of vibration in order to reduce chatter vibration in turning process. The device is composed of a linear oscillator corresponding to a flexible cutting tool subject to chatter strongly coupled to a Nonlinear Energy Sink (NES), with purely cubic stiffness. The novelty of this work is the use of a nonlinear cutting law, more accurate for modeling the cutting process. The delayed equations of motion are analyzed using a combination of the method of multiple scales and harmonic balance. Different types of responses regimes are revealed such as periodic response and also Strongly Modulated Response (SMR). Analytic results are then compared with numerical simulations. Finally, the potential of the NES is demonstrated to control chatter in turning process.
... Other methods used to control noise in the test status are presented. A modelling of the dynamic behaviour of a spindle supported by AMBs is made by Gourc et al. (2012). Authors have shown the importance of strong vibrations consideration. ...
High speed machining (HSM) is a new technology used to product parts in different sectors. This technology permits time and processing cost reduction. One of the principal components of the HSM is the spindle. It is generally supported by active magnetic bearings (AMBs), in order to guarantee the greatest speed without affecting the dynamic characteristics of the machine. In this paper, a spindle supported by two AMBs is modelled using the finite element method. It is discretised with Timoshenko beam finite element with different circular sections. Both flexible and rigid movements are taken into account. The non-linear electromagnetic loads exerted by bearings are computed in terms of the nominal air gap between bearings and spindle, the control current and the degrees of freedom of each node. A parametric study is performed to determine the influence of some parameters on the magnetic forces and subsequently the dynamic behaviour of the spindle.
