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
Tooth bending damage resulting from an intense impact by the rotor sometimes occurs in the transient operation.To investigate the influence of after-damage clearance and tooth bending length on the leakage performance...Tooth bending damage resulting from an intense impact by the rotor sometimes occurs in the transient operation.To investigate the influence of after-damage clearance and tooth bending length on the leakage performance and rotordynamic coefficients of labyrinth seals,three tooth bending damages were taken into consideration,including the unbent tooth damage(abbreviated as Unbent),the partial tooth bending damage(abbreviated as Pbent)and the complete tooth bending damage(abbreviated as Cbent).The transient CFD solution was utilized to calculate the leakage flow rates and rotordynamic coefficients of labyrinth seals with clearances of 0.3,0.4,0.5,0.6 mm for three tooth bending damages.The obtained result shows that the Unbent tooth damage leaks least while the Pbent tooth bending damage leaks most,and an increase of 6.1%for Cbent tooth bending damage and an increase of 19.4%for Pbent tooth bending damage are discovered at the tooth clearance of 0.6 mm in comparison with the Unbent tooth damage.Compared to the Unbent tooth damage,the effective damping for Pbent tooth bending damage and Cbent tooth bending damage is lower and drops by 9.7%–33.6%and 8.5%–22.6%respectively at the tooth clearance of 0.6 mm,suggesting that Pbent tooth bending damage or Cbent tooth bending damage tends to weaken the seal stability when compared to the Unbent tooth damage.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
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.
基金funded by the National Key R&D Program of China(No.2017YFB0601804)the National Natural Science Foundation of China(No.51776152)。
文摘Tooth bending damage resulting from an intense impact by the rotor sometimes occurs in the transient operation.To investigate the influence of after-damage clearance and tooth bending length on the leakage performance and rotordynamic coefficients of labyrinth seals,three tooth bending damages were taken into consideration,including the unbent tooth damage(abbreviated as Unbent),the partial tooth bending damage(abbreviated as Pbent)and the complete tooth bending damage(abbreviated as Cbent).The transient CFD solution was utilized to calculate the leakage flow rates and rotordynamic coefficients of labyrinth seals with clearances of 0.3,0.4,0.5,0.6 mm for three tooth bending damages.The obtained result shows that the Unbent tooth damage leaks least while the Pbent tooth bending damage leaks most,and an increase of 6.1%for Cbent tooth bending damage and an increase of 19.4%for Pbent tooth bending damage are discovered at the tooth clearance of 0.6 mm in comparison with the Unbent tooth damage.Compared to the Unbent tooth damage,the effective damping for Pbent tooth bending damage and Cbent tooth bending damage is lower and drops by 9.7%–33.6%and 8.5%–22.6%respectively at the tooth clearance of 0.6 mm,suggesting that Pbent tooth bending damage or Cbent tooth bending damage tends to weaken the seal stability when compared to the Unbent tooth damage.
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.
