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An active and passive control method is presented to suppress chatter vibrations of the spinning and cylindrical composite boring bar by combining the cutting process damping derived from indentation effect with piezoelectric damping stemmed from Macro Fiber Composite (MFC). The kinetic, potential and electrical energies of the composite boring bar based on the continuous distributed function are established by taking the constitutive relations of piezoelectric materials and the derivative feedback algorithm into account. Introducing the viscoelastic, the hysteretic, the process damping forces, the electrical field as well as cutting forces subjected to the boring process system and forming the virtual work of the non-conservative forces, a final nonlinear equation of motion is derived by utilizing extended Hamilton’s principle and Galerkin procedure. Afterward, the dynamic responses of composite boring bar are derived by using the method of multiple time scales. The proposed approach is validated by comparing the present results with those related papers. A combined model considering process damping effect and feedback gain is also confirmed. The influences of machining, internal and external damping and control parameters on vibration response and process stability of the novel composite boring bar are investigated and discussed. The nonlinear model proposed in this paper can assist in achieving optimal design for composite boring bar and improve the machinability of boring process.

We consider the dynamics of impact oscillators with multiple degrees of freedom subject to more than one motion limiting constraint or stop. A mathematical formulation for modeling such systems is developed using a modal approach including a modal form of the coefficient of restitution rule. The possible impact configurations for an N degree of freedom system are considered, along with definitions of the impact map for multiply constrained systems. We consider sticking motions that occur when a single mass in the system becomes stuck to an impact stop, and discuss the computational issues related to computing such solutions. Then using the example of a two degree of freedom system with two constraints we describe exact modal solutions for the free flight and sticking motions which occur in this system. Numerical examples of sticking orbits for this system are shown and we discuss identifying the region, S in phase space where these orbits exist. We use bifurcation diagrams to indicate differing regimes of vibro-impacting motion for two different cases; firstly when the stops are both equal and on the same side (i.e. the same sign) and secondly when the stops are unequal and of opposing sign. For these two different constraint configurations we observe qualitatively different dynamical behavior, which is interpreted using impact mappings and two-dimensional parameter space.

We consider the effect of random variation in the material parameters in a model for machine tool vibrations, specifically regenerative chatter. We show that fluctuations in these parameters appear as both multiplicative and additive noise in the model. We focus on the effect of additive noise in amplifying small vibrations which appear in subcritical regimes. Coherence resonance is demonstrated through computations, and is proposed as a route for transitions to larger vibrations. The dynamics also exhibit scaling laws observed in the analysis of general stochastic delay differential models.

We study complex dynamics of a cutting process, a recently developed frictional model of cutting process in [Rusinek et al., 2014] to gain better insight into the mechanics of frictional chatter and the factors affecting it. The new model takes into account the forces acting on the tool face as well as on the tool flank. We first present nonlinear dynamic behavior using bifurcation diagrams for nominal cutting depth and cutting velocity as the bifurcation parameters. Finally, the influence of the various forces on the tool flank on the system dynamics has been systematically studied. This has been performed by comparing the bifurcation diagrams with and without the forces on the flank. These flank forces have been found to largely have a stabilizing effect. These forces however increase the complexity of the solutions and are responsible for some instabilities in the low cutting velocity regime.

This paper studies the dynamics and bifurcations of a vibration-assisted, regenerative, nonlinear turning-tool system using an implicit mapping method. Machine vibration has been studied for a century for the improvement of machine accuracy and metal removal rate. In fact, this problem is unsolved yet. This is because such dynamical systems are involved in nonlinearity, discontinuity and time-delay. Thus, a comprehensive understanding of nonlinear machining dynamics with time-delay is indispensable. In this paper, period-$m$ motions in the turning machine-tool system are studied through specific mapping structures, and the corresponding stability and bifurcations of the period-$m$ motion are determined through the eigenvalue analysis. The analytical bifurcation scenarios for two sets of sequential period-$m$ motions in a turning-tool system are presented. Numerical simulations of period-$m$ motions are carried out to verify the prediction of periodic motions. The complex dynamics of vibration-assisted machining with strong nonlinearity are presented, which can provide a good overview for nonlinear dynamics of machine-tool systems.

Vibration is a mechanical phenomenon in which oscillations occur around an equilibrium point. In addition, the used and waste-cutting inserts create a great problem for the industry; therefore, these inserts constitute a problem to be solved in terms of both recycling and waste costs. The aim of this study is to analyze the correlation between vibration process parameters, formed during deep rolling, and surface roughness, micro-hardness with the using of the waste CBN inserts. For this, in total, 27 experiments in total were conducted with the help of a specially designed tool holder after parameters had been selected. The surface roughness, micro-hardness and vibration values of the specimens that were applied deep rolling were measured and the correlation between these values was investigated. When deep rolling was applied to the workpieces with used and waste CBN inserts, it was seen that the waste CBN inserts could be used in deep rolling and that the surface roughness improved and the surface hardness increased. In addition, it was seen that with the increase of the number of passes and rolling forces, the micro-hardness increased, and that feed rate, the number of passes and rolling forces had the biggest effect on vibration, respectively.

Considering the production requirement of workpiece optimization in order to reduce mass, the dynamic behavior of a workpiece can be affected. This factor can influence the performance of the milling process due to the occurrence of chatter vibrations. On the other hand, when the recommended cutting speed is relatively low, the tool rubs against the workpiece surface causing process damping. Consequently, the process becomes more stable and hence the depth of cut can be increased. In this paper, the stability of face milling of a cantilever plate at low cutting speed is investigated. The stability lobes diagram is determined numerically considering process damping. Cutting tests are conducted in order to verify the simulated results. An accelerometer is attached to the workpiece and its signal is measured and analyzed. Both workpiece surface and roughness are also investigated. The experimental results show a good agreement with the stability lobes diagram to predict the stable region under process damping. Hence, the depth of cut can be considerably increased, keeping the process stable at low cutting speeds.

Turning dynamics is investigated using a 3D model that allows for simultaneous workpiece-tool deflections in response to the exertion of nonlinear regenerative force. The workpiece is modeled as a system of three rotors connected by a flexible shaft. Such a configuration enables the motion of the workpiece relative to the tool and tool motion relative to the machining surface to be three-dimensionally established as functions of spindle speed, instantaneous depth-of-cut, material removal rate and whirling. The model is explored along with its 1D counterpart, which considers only tool motions and disregards workpiece vibrations. Different stages of stability for the workpiece and the tool subject to the same cutting conditions are studied.