In this paper,the response characteristics of dry friction backward whirl of a general rotor/stator model,which accounts for both the dynamics of the rotor and the stator as well as the friction and the deformation at...In this paper,the response characteristics of dry friction backward whirl of a general rotor/stator model,which accounts for both the dynamics of the rotor and the stator as well as the friction and the deformation at the contact surfaces,are investigated.The existence boundaries and the whirl frequencies of the dry friction backward whirl are determined analytically.It is found that there are two or three existence boundaries of the dry friction backward whirl that usually form two existence regions,either standing completely separately,or overlapping each other partly,or one containing the other completely,depending upon the system parameters.The whirl frequencies in the two existence regions are quite different and may jump between the lower and the higher values with the variation of the rotating speed.The results have been found to have good correspondence in the related rotor/stator rubbing experiments.展开更多
An incipient stage of a rotating drill string bit whirl motion proceeding on a well bottom surface is studied on the basis of kinematic （nonholonomic） models of mechanic interaction between the contacting uneven bod...An incipient stage of a rotating drill string bit whirl motion proceeding on a well bottom surface is studied on the basis of kinematic （nonholonomic） models of mechanic interaction between the contacting uneven bodies. The bit is considered to be an absolutely rigid spherical or ellipsoidal body, the well bottom surface can be plane or spherical. It is assumed that the system coaxiality is disturbed through small initial curvature of the drill string, imperfections of the bit and bore-well geometry or the system mass debalance. Linearized equations of the bit whirling are deducted, the frequencies of periodic motions are calculated, and their modes are constructed for different geometric parameters of the spherical and ellipsoidal bits. It is demonstrated that, depending on the system properties, the bit motion can acquire the regimes of forward and backward whMings or to transit to the state of stationary spinning relative to an immovable center of velocities. The most unfavorable and atypical whirling modes are characteristic for oblate eilipsoidal bits and curvilinear surfaces of the well bottom.展开更多
This paper deals with the theoretic simulation of a drill bit whirling under conditions of its contact interaction with the bore-hole bottom rock plane. The bit is considered to be an absolutely rigid ellipsoidal body...This paper deals with the theoretic simulation of a drill bit whirling under conditions of its contact interaction with the bore-hole bottom rock plane. The bit is considered to be an absolutely rigid ellipsoidal body with uneven surface. It is attached to the lower end of a rotating elastic drill string. In the perturbed state, the bit can roll without sliding on the bore-hole bottom, performing whirling vibrations (the model of dynamic equilibrium with pure rolling when maximum cohesive force does not exceed the ultimate Coulombic friction). To describe these motions, a nonholonomic dynamic model is proposed, constitutive partial differential equations are deduced. With their use, the whirling vibrations of oblong and oblate ellipsoidal bits are analyzed, the functions of cohesive (frictional) forces are calculated. It is shown that the system of elastic drill string and ellipsoidal bit can acquire stable or unstable whirl modes with approaching critical Eulerian values by the parameters of axial force, torque and angular velocity. The analogy of the found modes of motions with ones of the Celtic stones is established. It is shown that the ellipsoidal bits can stop their whirling vibrations and change directions of their circumferential motions in the same manner as the ellipsoidal Celtic stones do. As this takes place, the trajectories of the oblate ellipsoidal bits are characterized by more complicated paths and irregularities.展开更多
Transmission error(TE)in geared rotors is a predominant source of inherent excitation at the pitch point of the gear meshing.In this paper,a transverse vibration analysis is presented to study the effect of TE on gear...Transmission error(TE)in geared rotors is a predominant source of inherent excitation at the pitch point of the gear meshing.In this paper,a transverse vibration analysis is presented to study the effect of TE on geared rotors.Due to asymmetry in the TE,it is expected to have both forward and backward whirls excited during rotor whirling,which could be used for its detection.This aspect has been envisioned first time in the present work.To capture this,an approach of orienting the line of action of a gear-pair along oblique plane is considered and the mathematical modeling has been performed of a simple spur gear-pair connecting two parallel shafts at its mid-span with an asymmetric TE.To capture the forward and backward whirls,equations of motion are converted into a complex form that facilitates obtaining response in full spectrum.The response of system model with assumed transmission error and gear-pair parameters has been obtained through a numerical simulation,which shows distinctly the forward and backward whirls due to the TE.Through a simple test rig experimentation,a similar behaviour was observed in transverse vibrations of geared rotors in the full spectrum,which validate the proposed model.展开更多
基金supported by the National Natural Science Foundation of China (Grant Nos.10472086,10872155 and 10772140)
文摘In this paper,the response characteristics of dry friction backward whirl of a general rotor/stator model,which accounts for both the dynamics of the rotor and the stator as well as the friction and the deformation at the contact surfaces,are investigated.The existence boundaries and the whirl frequencies of the dry friction backward whirl are determined analytically.It is found that there are two or three existence boundaries of the dry friction backward whirl that usually form two existence regions,either standing completely separately,or overlapping each other partly,or one containing the other completely,depending upon the system parameters.The whirl frequencies in the two existence regions are quite different and may jump between the lower and the higher values with the variation of the rotating speed.The results have been found to have good correspondence in the related rotor/stator rubbing experiments.
文摘An incipient stage of a rotating drill string bit whirl motion proceeding on a well bottom surface is studied on the basis of kinematic （nonholonomic） models of mechanic interaction between the contacting uneven bodies. The bit is considered to be an absolutely rigid spherical or ellipsoidal body, the well bottom surface can be plane or spherical. It is assumed that the system coaxiality is disturbed through small initial curvature of the drill string, imperfections of the bit and bore-well geometry or the system mass debalance. Linearized equations of the bit whirling are deducted, the frequencies of periodic motions are calculated, and their modes are constructed for different geometric parameters of the spherical and ellipsoidal bits. It is demonstrated that, depending on the system properties, the bit motion can acquire the regimes of forward and backward whMings or to transit to the state of stationary spinning relative to an immovable center of velocities. The most unfavorable and atypical whirling modes are characteristic for oblate eilipsoidal bits and curvilinear surfaces of the well bottom.
文摘This paper deals with the theoretic simulation of a drill bit whirling under conditions of its contact interaction with the bore-hole bottom rock plane. The bit is considered to be an absolutely rigid ellipsoidal body with uneven surface. It is attached to the lower end of a rotating elastic drill string. In the perturbed state, the bit can roll without sliding on the bore-hole bottom, performing whirling vibrations (the model of dynamic equilibrium with pure rolling when maximum cohesive force does not exceed the ultimate Coulombic friction). To describe these motions, a nonholonomic dynamic model is proposed, constitutive partial differential equations are deduced. With their use, the whirling vibrations of oblong and oblate ellipsoidal bits are analyzed, the functions of cohesive (frictional) forces are calculated. It is shown that the system of elastic drill string and ellipsoidal bit can acquire stable or unstable whirl modes with approaching critical Eulerian values by the parameters of axial force, torque and angular velocity. The analogy of the found modes of motions with ones of the Celtic stones is established. It is shown that the ellipsoidal bits can stop their whirling vibrations and change directions of their circumferential motions in the same manner as the ellipsoidal Celtic stones do. As this takes place, the trajectories of the oblate ellipsoidal bits are characterized by more complicated paths and irregularities.
文摘Transmission error(TE)in geared rotors is a predominant source of inherent excitation at the pitch point of the gear meshing.In this paper,a transverse vibration analysis is presented to study the effect of TE on geared rotors.Due to asymmetry in the TE,it is expected to have both forward and backward whirls excited during rotor whirling,which could be used for its detection.This aspect has been envisioned first time in the present work.To capture this,an approach of orienting the line of action of a gear-pair along oblique plane is considered and the mathematical modeling has been performed of a simple spur gear-pair connecting two parallel shafts at its mid-span with an asymmetric TE.To capture the forward and backward whirls,equations of motion are converted into a complex form that facilitates obtaining response in full spectrum.The response of system model with assumed transmission error and gear-pair parameters has been obtained through a numerical simulation,which shows distinctly the forward and backward whirls due to the TE.Through a simple test rig experimentation,a similar behaviour was observed in transverse vibrations of geared rotors in the full spectrum,which validate the proposed model.
