This paper deals with the problem of limit cycles for the whirling pendulum equation x=y,y=sin x(cosx-r)under piecewise smooth perturbations of polynomials of cos x,sin x and y of degree n with the switching line x=0....This paper deals with the problem of limit cycles for the whirling pendulum equation x=y,y=sin x(cosx-r)under piecewise smooth perturbations of polynomials of cos x,sin x and y of degree n with the switching line x=0.The upper bounds of the number of limit cycles in both the oscillatory and the rotary regions are obtained using the Picard-Fuchs equations,which the generating functions of the associated first order Melnikov functions satisfy.Furthermore,the exact bound of a special case is given using the Chebyshev system.At the end,some numerical simulations are given to illustrate the existence of limit cycles.展开更多
A combined method of numerical simulation and field testing was adopted in this study in the interest of solving the problem of hard to control high concentrate dusts on a fully mechanized mining face. In addi- tion, ...A combined method of numerical simulation and field testing was adopted in this study in the interest of solving the problem of hard to control high concentrate dusts on a fully mechanized mining face. In addi- tion, the dust suppression effect of a multi-direction whirling air curtain was studied in this paper. Under the influence of the wall attachment effect, the compressed air which blows out from the two-phase or three-phase radial outlets on the generator of the air curtain can form a multi-direction whirling air curtain, which can cover the whole roadway section of a fully mechanized mining face. The traditional method of controlling dust is a forcing system with exhaust overlap which has the major disadvantage of lacking a jet effect and consequently results in poor dust control. It is difficult to form the air flow field within the range of Lp ≤ 5√S. However, due to the effect of this novel system, the radial airflow can be turned into axial airflow allowing fresh air to flow through the length of the heading. The air flow field which is good at controlling dust diffusion can be formed 12.8 m from the heading face. Furthermore, the field measurement results show that before the application of a multi-direction whirling air curtain, the dust concentration is 348.6 mg/m^3 and 271.4 mg/m^3 respectively at the roadway cross-section measurement points which are 5 m and 10 m from the heading face. However, after the application of the multi-direction whirling air curtain, the dust concentration is only 61.2 mg/m3 and 14.8 mg/m^3, respectively. Therefore, the dust control effect of a multi-direction whirling air curtain is obvious.展开更多
Over the last few decades,the research on the effect of bristle pack position on the rotordynamic characteristics of the brush-labyrinth seals is not sufficient.To this end,two kinds of brush-labyrinth seals for the b...Over the last few decades,the research on the effect of bristle pack position on the rotordynamic characteristics of the brush-labyrinth seals is not sufficient.To this end,two kinds of brush-labyrinth seals for the bristle pack element installed upstream of the labyrinth teeth named BSU and installed downstream of the labyrinth teeth called BSD were used to investigate the effect of bristle pack position on the rotordynamic characteristics of the brush-labyrinth seals.Using the numerical model combining the porous medium model and the whirling rotor method,the rotordynamic characteristics of the BSU and BSD at various operating conditions including four kinds of pressure ratios,five kinds of inlet preswirl speeds and four kinds of rotor spinning speeds were conducted.The obtained results show that the effects of operating conditions on rotordynamic coefficients for the different seal configurations are different.The direct stiffness,cross-coupled stiffness and direct damping of the BSU are lower than those of the BSD.The rotordynamic coefficients of the BSU are more insensitive to the operating conditions variation.From the perspective of the seal stability,the BSU is a better brush-labyrinth seal configuration at high pressure ratio,high positive preswirl or high rotor spinning speed conditions.While in the case of low pressure ratio,low positive preswirl or low rotor spinning speed conditions,the BSD is a better choice.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
Nonlinear dynamics of a cracked rotor with whirling were analyzed and were compared to a rotor without whirling. Distinct differences have been found in bifurcation, amplitude, orbit and Poincare map when carrying on ...Nonlinear dynamics of a cracked rotor with whirling were analyzed and were compared to a rotor without whirling. Distinct differences have been found in bifurcation, amplitude, orbit and Poincare map when carrying on this comparison. Complicated dynamics may be found when a cracked rotor has its whirling speed. The results revealed may be useful in crack-early-detection and diagnosis.展开更多
基金supported by the Natural Science Foundation of Ningxia(2022AAC05044)the National Natural Science Foundation of China(12161069)。
文摘This paper deals with the problem of limit cycles for the whirling pendulum equation x=y,y=sin x(cosx-r)under piecewise smooth perturbations of polynomials of cos x,sin x and y of degree n with the switching line x=0.The upper bounds of the number of limit cycles in both the oscillatory and the rotary regions are obtained using the Picard-Fuchs equations,which the generating functions of the associated first order Melnikov functions satisfy.Furthermore,the exact bound of a special case is given using the Chebyshev system.At the end,some numerical simulations are given to illustrate the existence of limit cycles.
基金supported by the Key Program of the Coal Joint Funds of the National Natural Science Foundation of China (No.U1261205)the Youth Program of National Natural Science Foundation of China (No.51404147)+2 种基金the Class General Financial Grant from the China Postdoctoral Science Foundation (No.2015M570601)the Scientific Research Foundation of Shandong University of Science and Technology for Recruited Talents (No.2014RCJJ029)the State Key Laboratory of Mining Disaster Prevention and Control Co-founded by Shandong Province and the Ministry of Science and Technology,Shandong University of Science and Technology (No.MDPC2013ZR02)
文摘A combined method of numerical simulation and field testing was adopted in this study in the interest of solving the problem of hard to control high concentrate dusts on a fully mechanized mining face. In addi- tion, the dust suppression effect of a multi-direction whirling air curtain was studied in this paper. Under the influence of the wall attachment effect, the compressed air which blows out from the two-phase or three-phase radial outlets on the generator of the air curtain can form a multi-direction whirling air curtain, which can cover the whole roadway section of a fully mechanized mining face. The traditional method of controlling dust is a forcing system with exhaust overlap which has the major disadvantage of lacking a jet effect and consequently results in poor dust control. It is difficult to form the air flow field within the range of Lp ≤ 5√S. However, due to the effect of this novel system, the radial airflow can be turned into axial airflow allowing fresh air to flow through the length of the heading. The air flow field which is good at controlling dust diffusion can be formed 12.8 m from the heading face. Furthermore, the field measurement results show that before the application of a multi-direction whirling air curtain, the dust concentration is 348.6 mg/m^3 and 271.4 mg/m^3 respectively at the roadway cross-section measurement points which are 5 m and 10 m from the heading face. However, after the application of the multi-direction whirling air curtain, the dust concentration is only 61.2 mg/m3 and 14.8 mg/m^3, respectively. Therefore, the dust control effect of a multi-direction whirling air curtain is obvious.
基金co-supported by the National Key R&D Program of China(No.2017YFB0601804)the National Natural Science Foundation of China(No.51776152)。
文摘Over the last few decades,the research on the effect of bristle pack position on the rotordynamic characteristics of the brush-labyrinth seals is not sufficient.To this end,two kinds of brush-labyrinth seals for the bristle pack element installed upstream of the labyrinth teeth named BSU and installed downstream of the labyrinth teeth called BSD were used to investigate the effect of bristle pack position on the rotordynamic characteristics of the brush-labyrinth seals.Using the numerical model combining the porous medium model and the whirling rotor method,the rotordynamic characteristics of the BSU and BSD at various operating conditions including four kinds of pressure ratios,five kinds of inlet preswirl speeds and four kinds of rotor spinning speeds were conducted.The obtained results show that the effects of operating conditions on rotordynamic coefficients for the different seal configurations are different.The direct stiffness,cross-coupled stiffness and direct damping of the BSU are lower than those of the BSD.The rotordynamic coefficients of the BSU are more insensitive to the operating conditions variation.From the perspective of the seal stability,the BSU is a better brush-labyrinth seal configuration at high pressure ratio,high positive preswirl or high rotor spinning speed conditions.While in the case of low pressure ratio,low positive preswirl or low rotor spinning speed conditions,the BSD is a better choice.
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Nonlinear dynamics of a cracked rotor with whirling were analyzed and were compared to a rotor without whirling. Distinct differences have been found in bifurcation, amplitude, orbit and Poincare map when carrying on this comparison. Complicated dynamics may be found when a cracked rotor has its whirling speed. The results revealed may be useful in crack-early-detection and diagnosis.
