Nonlinear Dynamics Behaviors of a Rotor Roller Bearing System with Radial Clearances and Waviness Considered

A rotor system supported by roller beatings displays very complicated nonlinear behaviors due to nonlinear Hertzian contact forces, radial clearances and bearing waviness. This paper presents nonlinear bearing forces of a roller bearing under four-dimensional loads and establishes 4-DOF dynamics equations of a rotor roller bearing system. The methods of Newmark-β and of Newton-Laphson are used to solve the nonlinear equations. The dynamics behaviors of a rigid rotor system are studied through the bifurcation, the Poincar è maps, the spectrum diagrams and the axis orbit of responses of the system. The results show that the system is liable to undergo instability caused by the quasi-periodic bifurcation, the periodic-doubling bifurcation and chaos routes as the rotational speed increases. Clearances, outer race waviness, inner race waviness, roller waviness, damping, radial forces and unbalanced forces-all these bring a significant influence to bear on the system stability. As the clearance increases, the dynamics behaviors become complicated with the number and the scale of instable regions becoming larger. The vibration frequencies induced by the roller bearing waviness and the orders of the waviness might cause severe vibrations. The system is able to eliminate non-periodic vibration by reasonable choice and optimization of the parameters.

Effectof Film Force Nonlinearity on Unbalance Responseof a Jeffcot RotorJournal Bearing System

The effect of oil film force nonlinearity on unbalance response of Jeffcot rotor elliptical bearing system is studied. Linear analysis is done by linearizing the bearing oil film dynamic forces and expressing them with stiffness and damping constants. Nonlinear dynamic simulation is done by taking the nonlinearity of bearing oil film dynamic force into full consideration, with the latter being expressed by a special database which is generated beforehand, and based on non stationary Reynolds equation and Reynolds boundary condition of film rupture. The linear and nonlinear unbalance responses of a Jeffcot rotor supported on a pair of elliptical bearings is studied. The resulting dynamic characteristics and rotor and journal whirling orbits are compared. While good consistancy between nonlinear and linear predictions is found under very small unbalance, significant or even drastic differences are found whenever the unbalance is not small, indicating the necessity of including the nonlinearity of oil film dynamic forces, especially when response to large unbalance is to be predicted.

Nonlinear dynamic behaviors of ball bearing rotor system

Nonlinear forces and moments caused by ball bearing were calculated based on relationship of displacement and deflection and quasi-dynamic model of bearing.Five-DOF dynamic equations of rotor supported by ball bearings were estimated.The Newmark-β method and Newton-Laphson method were used to solve the equations.The dynamic characteristics of rotor system were studied through the time response,the phase portrait,the Poincar?maps and the bifurcation diagrams.The results show that the system goes through the quasi-periodic bifurcation route to chaos as rotate speed increases and there are several quasi-periodic regions and chaos regions.The amplitude decreases and the dynamic behaviors change as the axial load of ball bearing increases;the initial contact angle of ball bearing affects dynamic behaviors of the system obviously.The system can avoid non-periodic vibration by choosing structural parameters and operating parameters reasonably.

An Improved Design of Spiral Groove Mechanical Seal

The coupling effect among the flow of fluid film, the frictional heat of fluid film and the thermal deformation of sealing rings is inherent in mechanical seals. The frictional heat transfer analysis was carded out to optimize the geometrical parameters of the sealing rings, such as the length, the inner radius and the outer radius. The geometrical parameters of spiral grooves, such as the spiral angle, the end radius, the groove depth, the ratio of the groove width to the weir width and the number of the grooves, were optimized by regarding the maximum bearing force of fluid film as the optimization objective with the coupling effect considered. The depth of spiral groove was designed to gradually increase from the end radius of spiral groove to the outer radius of end face in order to decrease the weakening effect of thermal deformation on the hydrodynamic effect of spiral grooves. The end faces of sealing rings were machined to form a divergent gap at inner radius, and a parallel gap will form to reduce the leakage rate when the thermal deformation takes place. The improved spiral groove mechanical seal possesses good heat transfer performance and sealing ability.

Effects of bottom bracings on torsional dynamic characteristics of horizontally curved twin I-girder bridges with different curvatures

Curved twin I-girder bridges (CTIGBs) have low torsional stiffness that makes them vulnerable to dynamic loads. This study investigates the effects of bottom bracings on the torsional dynamic characteristics of CTIGBs. Five types of bottom bracings are designed to investigate their effects on the dynamic characteristics of CTIGBs with different curvatures under free and forced vibrations. To perform numerical investigations, three-dimensional (3-D) finite element (FE) bridge and vehicle models are established using commercial ANSYS code, and then a vehicle-bridge interaction analysis approach is proposed. Road roughness profiles generated from power spectral density and cross spectral functions are also taken into account in the analyses. The numerical results show that torsional frequencies increase significantly after providing bottom bracings, and the increasing rate depends on the type of bottom bracings and their locations of installation. Bottom bracings can act as load transmitting members from one main girder to the others. Large negative bearing forces that have occurred in bridges with small radii of curvatures can be remarkably reduced by providing bottom bracing systems. It is found that the performances of several bottom bracing systems are effective in improving the torsional dynamic characteristics of the bridges in this study.

CHARACTERISTCS OF FLUID FILM IN OPTIMIZED SPIRAL GROOVE MECHANICAL SEAL

In order to investigate the sealing performance variation resulted from the thermal deformation of the end faces, the equations to calculate the fluid film pressure distribution, the bearing force and the leakage rate are derived, for the fluid film both in parallel gap and in wedgy gap. The geometrical parameters of the sealing members are optimized by means of heat transfer analysis and complex method. The analysis results indicate that the shallow spiral grooves can generate hydrodynamic pressure while the rotating ring rotates and the bearing force of the fluid film in spiral groove end faces is much larger than that in the flat end faces. The deformation increases the bearing force of the fluid film in flat end faces, but it decreases the hydrodynamic pressure of the fluid film in spiral groove end faces. The gap dimensions which determine the characteristics of the fluid film is obtained by coupling analysis of the frictional heat and the thermal deformation in consideration of the equilibrium condition of the bearing force and the closing force. For different gap dimensions, the relation- ship between the closing force and the leakage rate is also investigated, based on which the leakage rate can be controlled by adjusting the closing force.

Effects of AMB Parameters on the Dynamic Stability of the Rotor

The motion equation of the rotor suspended by active magnetic bearing (AMB)is given in this paper after considering the nonlinear characteristics of the force.Fromthe response equation resulted from this Eq.we gained the functions of the jump ra-nge,and examined the effects of the A MB's parameters.

Impact of bending dies with different friction forms on forming force and quality of tubes manufactured by free bending technology

In the 3 D free bending forming system,the bending die can be designed either in a sliding type or rolling friction type.Bending die-based sliding friction type is often called normal bending dies;however,the bending dies-based rolling friction type includes bending die-based roller type and ball type in structure.In the current study,the impact of three bending dies on the forming force,and the bent tube quality was investigated.The obtained results showed that the tangential stresses and strains of the tubes formed by the bending die-based roller type were the smallest among the three bending dies.Besides,the spherical bearing force PUwas reduced drastically after using the roller type and ball type compared to the sliding friction type.Moreover,the uniformity of the wall thickness distribution of the tubes formed by the roller type and ball type was better than those obtained from the sliding friction type.In addition,the cross-section distortion rate was reduced by 2.8%using the roller type,and 1.8%using ball-type compared to the sliding friction type.