Automatic Balancing of Rotor Bearing Systems

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214 Advances on Analysis and Control of Vibrations Theory and Applications. 2002 Green et al 2008 Guozhi et al 2000 Hredzak et al 2006 Sheu et al 1997 Zhou y Shi. 2001 2002 These active balancing control schemes require information of the eccentricity of. the involved rotating machinery On the other hand there exists a vast literature on. identification and estimation methods which are essentially asymptotic recursive or. complex which generally suffer from poor speed performance see e g Ljung 1987. Soderstrom 1989 and Sagara and Zhao 1989 1990, Passive semi active and active control schemes have been proposed in order to cancel or. attenuate the vibration amplitudes in rotating machinery In passive control the rotating. machinery is modified off line e g the rotor is stopped to adjust some of its parameters such. as mass stiffness or damping Balancing consist of placing correction masses onto the. rotating shaft inertial disk so that centrifugal forces due to these masses cancel out those. caused by the residual imbalance mass, Active vibration control AVC changes the dynamical properties of the system by using. actuators or active devices during instantaneous operating conditions measured by the. appropriate sensors The main advantage of active control compared to passive control is. the versatility in adapting to different load conditions perturbations and configurations of. the rotating machinery and hence extending the system s life while greatly reducing. operating costs, Semiactive vibration control devices are increasingly being investigated and implemented. These devices change the system properties such as damping and stiffness while the rotor is. operating This control scheme is based on the analysis of the open loop response Semi. active control devices have received a great deal of attention in recent years because they. offer the adaptability of active control without requiring the associated large power sources. This chapter deals with the active cancellation problem of mechanical vibrations in rotor. bearing systems The use of an active disk is proposed for actively balancing a rotor by. placing a balancing mass at a suitable position Two nonlinear controllers with integral. compensation are proposed to place the balancing mass at a specific position Algebraic. identification is used for on line eccentricity estimation as the implementation of this active. disk is based on knowledge of the eccentricity An important property of this algebraic. identification is that the eccentricity identification is not asymptotic but algebraic in contrast. to most of the traditional identification methods which generally suffer of poor speed. performance In addition a velocity control is designed to drive the rotor velocity to a. desired operating point during the first critical speed. The proposed results are strongly based on the algebraic parameter identification approach. for linear systems reported in Flies and Sira 2003 which requires a priori knowledge of. the mathematical model of the system This approach has been used for parameter and. signal estimation in nonlinear and linear vibrating mechanical systems where numerical. simulations and experimental results show that the algebraic identification provides high. robustness against parameter uncertainty frequency variations small measurement errors. and noise Beltran et al 2005 2006 2010,Automatic Balancing of Rotor Bearing Systems 215. 2 Active balancing and vibration control of rotating machinery. Many methods for passive balancing have been proposed such as single plane two planes. or multi plane balancing These off line balancing methods are very common in industrial. applications In these methods the rotor is modeled as a rigid shaft that without elastic. deformation during operation Rotors operating under 5000 rpm can be considered rigid. rotors For flexible rotors the modal balancing and influence coefficient methods were. developed for off line balancing Figure 1 shows an inertial disk to be balanced by adding a. mass in opposite direction to compensate the residual unbalance. Figure 1 Inertial disk and eddy current probe displacement sensor. Thearle Thearle 1932 developed a machine for dynamically balancing rotating elements or. high speed rotors figure 2 where an out of balance mass of a rotating element or body can. quickly and easily be located providing the exact amount and location of the balancing mass. that should be placed or removed to reduce the vibration The balancing machine contains a. balancing head with a clutch which is first opened to release a set of balls to naturally take. place in the balancing positions Subsequently the clutch is closed producing a clamping of the. balls in the adjusted positions while the body is being rotated above its critical speed and then. released Other automatic balancing devices have been proposed essentially using one of the. four balancing methods two angular arms two sliding arms one angular and sliding arm or. one spirally sliding arm Chong Won 2006 Zhou y Shi 2001. Figure 2 Diagram of the automatic balancer using two masses. 216 Advances on Analysis and Control of Vibrations Theory and Applications. The use of piezoelectric actuators as active vibration dampers in rotating machines has been. considered in the past Palazzolo et al Palazzolo et al 1993 first used the piezoelectric. pusher for active vibration control in rotating machinery as it is shown in Figure 3 a The. pusher is soft mounted to the machine case to improve the electromechanical stability and. connected to the squirrel cage ball bearing supports of a rotating shaft to actively control. the unbalance transient and subsynchronous responses of the test rotor using velocity. feedback The piezoelectric actuators are modeled as dampers and springs Recently. Carmignani et al Carmignani et al 2001 developed an adaptive hydrodynamic bearing. made of a mobile housing mounted on piezoelectric actuators to attenuate the vibration. amplitudes in constant speed below the first critical speed The actuators arranged at 90 on. a perpendicular plane to the shaft axis exert two sinusoidal forces with a tuned phase angle. to produce a balancing or alternatively a dampering effect The authors presented. experimental and numerical results, Active Magnetic Bearings AMBs are the mostly used devices but their use in the industrial.
field is still limited due to a low stiffness and the need of additional conventional bearings. for fault emergency An AMB system is a collection of electromagnets used to suspend an. object and stabilization of the system is performed by feedback control see Figure 3 b In. recent decades AMBs has been widely used as a non contact lubrication free support in. many machines and devices Many researchers Lee 2001 Sheu Yang 1997 have proposed. a variety of AMBs that are compact and simple structured The AMB system which is open. loop unstable and highly coupled due to nonlinearities inherited in the system such as the. gyroscopic effect and imbalance requires a dynamic controller to stabilize the system. Figure 3 a Piezoelectric actuator and b active magnetic bearing. Another device for AVC in rotating machinery is the one based on fluid film bearings The. dynamics of a rotor system supported by fluid film bearings is inherently a nonlinear. problem and these fluid film bearings have been used in combination with other devices. such as piezoelectric actuators magneto or electro rheological fluids etc see Figure 4. Guozhi et al 2000 proposed the use of a fluid bearing with rheological fluids to reduce the. vibrations around the first critical speed Magnetorheological MR or electrorheological. Automatic Balancing of Rotor Bearing Systems 217, ER fluids are materials that respond to an applied magnetic or electric field with a. dramatic change in rheological behavior To attenuate the vibration amplitudes around the. first critical speed an on off control is proposed to control the large amplitude around the. first critical speed, Hathout and El Shafei Hathout and El Shafei 1997 proposed a hybrid squeeze film. damper HSFD see Figure 4 b to attenuate the vibrations in rotating machinery for both. sudden unbalance and transient run up through critical speeds El Shafei El Shafei 2000. have implemented different control algorithms PID type controllers LQR gain scheduling. adaptive and bang bang controllers for active control of rotor vibrations for HSFD. supported rotors Controlling the fluid pressure in the chamber the bearing properties of. stiffness and damping can be changed,Electrorheological Fluid inlet Sealed. fluid chamber,Ball Spring,bearing rotor, Figure 4 Fluid film bearings a using rheological fluids and b using a pressure chamber. Sun y Kroedkiewski Sun and Krodkiewski 1997 1998 proposed a new type of active oil. bearing see Figure 5 a The active bearing is supplied with a flexible sleeve whose. deformation can be changed during rotor operation The flexible sleeve is also a part of a. hydraulic damper whose parameters can be controlled during operation as well The oil film. and the pressure chamber are separated by the flexible sealing The equilibrium position of. the flexible sleeve and the bearing journal is determined by load and pressure which can be. controlled during operation Parameters of this damper can also be varied during operation. to eliminate the self exciting vibration and increase the stability of the equilibrium position. of the rotor oil bearing system, Recently Dyer et al Dyer et al 2002 developed an electromagnetically actuated.
unbalance compensator The compensator consists of two rings as shown in Figure 5 b. These two rings are not balanced and can be viewed as two heavy spots These two rings are. held in place by permanent magnetic forces When the balancer is activated an electric. current passes through the coil and the rings can be moved individually with respect to the. spindle by the electromagnetic force The combination of these two heavy spots is. equivalent to a single heavy spot whose magnitude and position can change to attenuate the. vibration amplitudes, 218 Advances on Analysis and Control of Vibrations Theory and Applications. Figure 5 a Fluid film bearing with flexible sleeve and b electromagnetically actuated unbalance. compensator,3 Rotor bearing system,3 1 Mathematical model. The rotor bearing system consists of a planar and rigid disk of mass M mounted on a. flexible shaft of negligible mass and stiffness k at the mid span between two symmetric. bearing supports see Fig 6 when a b Due to rotor imbalance the mass center is not located. at the geometric center of the disk S but at the point G center of mass of the unbalanced. disk the distance between these points is known as disk eccentricity or static unbalance u. see Vance 1988 Dimarogonas 1996,Figure 6 Rotor bearing system with active disk. In the analysis the rotor bearing system has an active disk Blanco et al 2008 mounted on. the shaft and near the main disk see Fig 6 The active disk is designed in order to move a. mass in all angular and radial positions inside of the disk given by and respectively. In fact these movements can be obtained with some mechanical elements such as helical. gears and a ball screw see Fig 7 a The mass and the radial distance are designed in. order to compensate the residual unbalance of the rotor bearing system by means of the. correct angular position of the balancing mass The angular position of the unbalance is. denote by see Fig 7 b,Automatic Balancing of Rotor Bearing Systems 219. Figure 7 Schematic diagram and main elements of the active disk. The mathematical model of the five degree of freedom rotor bearing system with active. disk was obtained using Euler Lagrange equations which is given by. sin cos sin cos,sin cos sin cos,sin cos sin cos, Here c is the equivalent viscous damping provided by the isotropic bearings and.
are the inertia polar moment and the viscous damping of the rotor respectively is. the applied torque control input for rotor speed regulation and are the orthogonal. coordinates that describe the disk position and denote the radial and angular. positions of the balancing mass which is controlled by means of the control force. and the control torque servomechanism The angular position of the rotor is denote. Defining the state variables as, and the following state space description is obtained. 220 Advances on Analysis and Control of Vibrations Theory and Applications. The rotor bearing system with active disk is then described by the five degree of freedom. highly nonlinear and coupled model 2 The proposed control objective consists of reducing. as much as possible the rotor vibration amplitude denoted in non dimensional units by. for run up coast down or steady state operation of the rotor system even in presence of. small exogenous or endogenous perturbations, In the following table the rotor system parameters used throughout the chapter are presented. 1 2 0 003 0 3,100 1 5 10 0 01,Table 1 System parameters. Automatic Balancing of Rotor Bearing Systems 221,3 2 Active vibration control. 3 2 1 Active disk control, Here it is proposed to use an active disk for actively balancing of the rotor see Fig 8 It can.
be seen that if the mass is located at the position the unbalance can. be cancelled because the centrifugal force due to this mass cancel out those caused by the. Automatic Balancing of Rotor Bearing Systems 217 ER fluids are materials that respond to an applied magnetic or electric field with a dramatic change in rheological behavior To attenuate the vibration amplitudes around the first critical speed an on off control is proposed to control the largeamplitude around the first critical speed

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