| 1.IntroductionWith development of modern industry and the industrial technology progress, structure and machinery become more flexible, and the need for higher part accuracy is urgent, but ,chatter is one of the main factor that affecting machining accuracy, so, how to resolve this problem has become a challenging subject. Boring is a finish machining operation, it is more important to avoid chatter in boring process.Piezoelectric ceramic is used as active control element in the paper, and the Genetic Algorithm is also applied to solve the optimal placement of piezoelectric sensors/actuators in boring bar. According to the different designing case of boring bar, its equivalent lumped mass model and finite element model are discussed respectively. Then the regenerative chatter occurred in boring bar is effectively suppressed by using active control method in emluator.2.Piezoelectric TheoryPiezoelectric crystals are made to be patches that have different shapes. These crystals are called vibrator. They can be in different electricity boundary condition and in mechanical boundary condition due to different applied state or testing state. When they are in different conditions, the chosen individual variables are different. Beam bonded with piezoelectric actuators and sensors is one-dimensional structural control problem, so, piezoelectric equation can be expressed asWhereσ1 denote the stress in x direction,ε1 is the strain in x direction, E3, the intensity of electric field in z direction, D3 ,the electric displacement in z direction.The piezoelectric stack can meet the demand of practical using, which can generate suitable displacement and bear some amount of load. The method is to stack a number of piezoelectric ceramics, connecting their electrodes electrically in parallel. The result is that for n layers of stacked PZT the actuator produces n times more displacement.So, the driving voltage for each unit is U, each displacement,ΔLi is the same in amplitude and phase, the total displacement can be written as Where Ks=(ki)/n, it is equivalent mechanics stiffness, ds = nd33 , it is equivalent piezoelectric coefficient. k iis piezoelectric stiffness.And, the output of piezoelectric sensors/actuators can also be added, Where Cs = nCi, it is the stack capacitance; Ci is piezoelectric equivalent capacitance. Equation (1) and (2) reflect the basic design principle of piezoelectric stack sensor/actuator.3.Emulation Research on Active Chatter Control of Boring Bar with Active Dynamic AbsorberPiezoelectric ceramics are applied to control chatter phenomenon in boring bar, boring bar can be assumed to be a lumped mass model, so, the actuator force produced by piezoelectric stack acts as an inertial force that counteracts the disturbance on the main system. According to the work made by scholars on boring bar chatter and the boring bar mechanism designed by Baker, an equivalent lumpedmass model of a boring bar is considered, a piezoelectric transducer (PT) is used to control the system.A tensile force in the PT results in a positively-valued Fp,and it acts in the + y1 direction on the main mass of Figure 1,and it acts in the -y2 direction on the secondary mass. The equations of motion for the system of Figure 1 are, thereforeUsing the state variables , rearranging,Where [A] is a 4×4 matrice,In order to use the absorber mass to improve boring bar stability, it is very important that any information related to the cutting process, but, taking the difficulty in accurately modeling the cutting process into account, the idea is to supply, at any time, an appropriate voltage to the PT so that its deformation affects the overall bar in such a way that the motion of the tip of the bar is minimized. So, applying linear quadratic regulator (LQR) to calculate an optimal control voltage is considered.4.The placement optimization of piezoelectric sensors/actuatorsGenetic algorithm (GA) provides a universal frame for solving the optimization problem on multi-objective, multi-model nonlinear complex system, It is widely used because of it does not depend on any field that the problem belongs to.Firstly, finding a objective function in order to use GA, the final objective function must contain the information about the placement and gain of actuators. It is assumed that the piezoelectric patches are sticked from the clamped end to the free end of the beam, and they can not be overlapped, therefore, the nonlinear optimization model of the cantilever is given byWhere, j is the j th pair of the piezoelectric ceramics, m denotes there are m pairs actuators, xj1, xj2 are the distance from the left of the patch to the clamped end and the right of the patch to the clamped one respectively;The objective function is converted into the fitness function required by GA, for objective function min J = tr(P), it can be written asApplying the repeated selection, crossover and mutation to find a fittest value, the value is the optimal result.5.Active control research on boring chatter based on finite element methodThe control of cantilever beam surface-bonded with piezoceramic actuators/sensors showed in Fig.2 is considered. The piezoelectric actuators/sensors are placed symmetrical along the neutrosphere of the beam, so, they can be treated as an finite unit, the dynamic equation of the system is written asWhere the subscript (.)e is used to denote the beam element, (FD)e denotes the external forces acting on the element, (FC)e represents the control forces due to the piezoelectric actuator, and the displacement vector ue is given byThe element matrices can be assembled to yield the system equations of motionThe above equation can be rewritten in the state variable form required for the derivation of optimal feedback controlWhere the dimension N = 2n, the actuators/sensors location matrices respectively. The measurement vector y corresponds to the measured sensor voltages US(t), and the control input f is related to the control voltages applied to the actuator patches. The control input f is given by fT = {0 VaT(t)}.6. ConclusionAfter placement optimization of piezoelectric patches by using GA, the emulation research on active control of the generative chatter in boring bar is implemented, the result demonstrates the control effect is pretty good.Fig.5. the distance after amplifying the gain of controller...
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