| 1. IntroductionAll objects which have elasticity and quality can be vibratile. Vibration and noise have the enormous influence on the performance of mechanical system, operator's physical and moral integrity as well as the processing quality, and so on;It's an important problem in the field of technology about how to prevent and control vibration effectively. Boring processing is at half seal condition, the boring bar extends longways, and the back surface of the cutter has a big friction with the inner hole, which can result in the non-steady state of the system and vibration easily. Therefore, it's very important and urgent to control the vibration in the course of the boring process.In this paper an intelligent boring spindle is designed and hoped to reduce the chatter when processing, which can carry out the active vibration control of the boring process. The theories of piezoelectric intelligent structures and active vibration control (AVC) are dissertated, with that designed the direct-current amplifying circuit in this foundation and constructed the AVC system of intelligent boring bar. Moreover, the effect of suppressing vibration has been confirmed with the experiment.2. Piezoelectric Equation and establishment of sensing and actuating modelPiezoelectric ceramics have the function of exchanging "mechanical energy"and "electrical energy"(fig 1).Piezoelectric Effectelectrical energymechanical energyConversePiezoelectric EffectFigl Piezoelectric electromechanical transducer The basic characteristics of piezoelectric ceramics include: (D Displacement characteristic.(2) Stress - displacement characteristic. 0(3) Temperature characteristic, which mainly includes line inflation characteristic and the influence on the piezoelectric effect by temperature.(D Sluggish characteristic.Piezoelectric equation is the relation between crystal's mechanical quantity (stress tensor T and strain tensor S) and the electricity quantity (electric-field intensity E and electric displacement D), simultaneously these quantities also concern with the calorifics quantities (temperature and entropy). Piezoelectric equation is called piezoelectric relation between the reality and the structure.Referring to the piezoelectric vibrator as the intelligent part, it always is in the second kind of boundary condition, namely the machinery supports on both sides with the electricity short-circuits. Chooses the strain and the electric-field intensity as the independent variable, the stress and the electric displacement as the dependent variable to indicate the interwork of the electric behavior and the mechanic one ,and we find the second piezoelectric equation. We can derive the piezoelectric equation by the first law of thermodynamicsD = e-S + es -E (1)T=CE S-eT E (2)In this formula, CE is the elastic rigidity constant matrix when electric-field intensity E is zero, e s is the dielectrical constant matrix when strain S is zero (orconstant), and e is the piezoelectricity stress constant matrix;eT is thetransposed matrix of e. The type (1) is called the piezoelectric equation of piezoelectric effect, and the type (2) is called the piezoelectric equation of converse piezoelectric effect.The sensing equation of the piezoelectric intelligent beam in the condition of two-sided gluing the piezoelectric sensor/actuator isAnd2 '[Jin 31So=bs -d31 -Ys .^L.—(3)In this formula, dn is the piezoelectric modulus (piezoelectricity stress constant), its unit is Meter/Volt;Ys is the Yang module of the piezoelectric sensor,it's unit is Newton/Meter2;hs and hb are the thickness of the piezoelectric sensor and the main body, andsensorkactuatorFig2 the intelligent beam section gluing piezoelectric actuator and sensor When the piezoelectric piece is used as actuator, it will act on the mainbody beam. Neglecting the influence of the axial force, M(x,t) isThereintod2W. 1dx2/ 2 2\SoM(x,t)d2w\ ?.. , . ? . K +hhYJ(x) -— \-V{x,t)-d3l-Y.-b3-dx2[H(x-Xn)-(x-Xi2)]The type is called the actuating equation of the piezoelectric actuator.Fig 3 is the distributed force model of the piezoelectric intelligent beam concerning on the influence of the gluing layer. Because the thickness of the gluing layer is thinner than the beam and the piezoelectric piece, we neglect the sticky and elastic effect of it. According to the strength balanced relationship in x axisEb\. k-ydy+Ej k-ydy+EaC (k-y-A)dy = 0In this formula, Eb, Es and Ea are respectively the Yang modules of thebeam, gluing layer and the actuating layer. tb,ts and ta are respectively thethickness of the beam, gluing layer and the actuating layer. So2KRbb[Ebtl + 2Ejt. [t2s +12a2)+ 2Eja (t2 +12b2)\ 3f[W/? +4W,(/J, +Rs)+4{Rb+2Rs +l)JThe type (4) is called the distributed force model in the condition of two-sided gluing the piezoelectric sensor/actuator.Z "beam■■■t.Fig3 the distributed force model in the condition of two-sided gluing thepiezoelectric sensor/actuator 3. Study on the Piezoelectric Actuator and The Actuating MethodsThe key point of the AVC is the designing of the actuating system. Among them, the piezoelectric actuator and it's actuating methods are the most important parts. Piezoelectric actuating technique is the extension and development of the piezoelectricity in mechanical domain. It's progress depends on the development of he material study, electronics, the mechanical mechanics, the empirical science and so on.Using PZT as the actuator applies its converse piezoelectric effect. The commonly piezoelectric actuator has two types: multilayer piezoelectric actuators and the 2-DOF inertial impact piezoelectric actuator prototype.The actuating circuit designed by the author is like Fig 4 shows.Fig4 piezoelectric actuating circuitFig5 shows its theory.Fig5 Theory picture of piezoelectric actuating circuit 4. The Experiment and Analysis of Intelligent Boring SpindleThe experiment was executed on a general lathe CA6140. The experiment equipments for the intelligent boring spindle are expressed as Fig6.Computersensorhigh voltage drive power supplyFeedback ControllerFig6 System setting picture Experiment condition:(l)The testing material: 45# steel, the external hole diameterD = (f>95mm , the internal hole diameter d = |
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