Interaction of a Whirling Rotor with a Vibrating Stator across a Clearance Annulus

1968 ◽  
Vol 10 (1) ◽  
pp. 1-12 ◽  
Author(s):  
H. F. Black
Keyword(s):  
Dry Friction ◽  
Ball Bearing ◽  
Radial Symmetry ◽  
Experimental Results ◽  
Equilibrium Conditions ◽  
General Behaviour ◽  
Mass Unbalance ◽  
Jump Phenomena ◽  
Rotor Stator Interaction ◽  
Rotor Mass

Where a rotor runs within a clearance space, the clearance being comparable with rotor mass unbalance, the synchronous whirling behaviour of the rotor may be considerably affected by intermittent interaction with the stator at the clearance position. Discontinuity and jump phenomena may occur: in general, behaviour will be different with increasing speed from that with decreasing speed, and in either case zones may exist in which rotor-stator interaction is possible but not certain. In the analysis here presented, rotor and stator are regarded as linear multi-degree-of-freedom systems including damping; dry friction at the clearance space is taken into account. Discussion is limited to cases with radial symmetry, and interaction is assumed limited to the position of the clearance space. Polar receptances are used to establish equilibrium conditions with interaction, and speed zones are defined within which interaction may occur. Some hypothetical cases are fully explored, demonstrating that rotor-stator interactions may occur in a variety of forms and circumstances. Interactions with dry friction counterwhirling are also considered. Some experimental results on counterwhirl within a ball bearing are given and qualitatively compared with theory.

Rotor/Seal Experimental and Analytical Study on Full Annular Rub

2002 ◽  
Vol 124 (2) ◽  
pp. 340-350 ◽  
Author(s):  
J. J. Yu ◽  
P. Goldman ◽  
D. E. Bently ◽  
A. Muzynska
Keyword(s):  
Mathematical Model ◽  
Dry Friction ◽  
Analytical Study ◽  
Experimental Results ◽  
Triggering Mechanism ◽  
Mass Unbalance ◽  
Destabilizing Factors ◽  
Small Clearance ◽  
Nonlinear Solutions ◽  
Simplified Mathematical Model

Rotor/seal full annular rub, including synchronous (forward) and reverse (backward) precessions, has been investigated both experimentally and analytically. Of particular interest is the finding of reverse precessional full annular rub (dry whip) that occurs repeatedly in small clearance cases without any outside disturbance. The experimental results include rub triggering mechanism, mass unbalance, and rotative speed effects. A simplified mathematical model is used to interpret experimental results. Nonlinear solutions for both synchronous and reverse precessions are obtained along with instability zones. Mass unbalance effect on shifting from synchronous response to reverse rub and destabilizing factors such as dry friction, rotor damping, and seal stiffness, are discussed.

Rotor/Seal Experimental and Analytical Study on Full Annular Rub

2000 ◽  
Author(s):  
John J. Yu ◽  
Paul Goldman ◽  
Donald E. Bently
Keyword(s):  
Mathematical Model ◽  
Dry Friction ◽  
Analytical Study ◽  
Experimental Results ◽  
Triggering Mechanism ◽  
Mass Unbalance ◽  
Destabilizing Factors ◽  
Small Clearance ◽  
Nonlinear Solutions ◽  
Simplified Mathematical Model

Rotor/seal full annular rub, including synchronous (forward) and reverse (backward) precessions, has been investigated both experimentally and analytically. Of particular interest is the finding of reverse precessional full annular rub (dry whip) that occurs repeatedly in small clearance cases without any outside disturbance. The experimental results include rub triggering mechanism, mass unbalance, and rotative speed effects. A simplified mathematical model is used to interpret experimental results. Nonlinear solutions for both synchronous and reverse precessions are obtained along with instability zones. Mass unbalance effect on shifting from synchronous response to reverse rub and destabilizing factors such as dry friction, rotor damping, and seal stiffness, are discussed.

Nonlinear Dynamic Response Analysis of Rotor-Ball Bearing-Stator Coupling System Including Unbalance-Rubbing Coupling Faults

2007 ◽  
Author(s):  
Guo Chen ◽  
Rong Tao Hou
Keyword(s):  
Ball Bearing ◽  
Dynamic Responses ◽  
Response Analysis ◽  
Nonlinear Dynamic Response ◽  
Rotating Speed ◽  
Coupling Faults ◽  
Mass Unbalance ◽  
Coupling System ◽  
Chaos Motion ◽  
Rotor Mass

In this paper, a new rotor-ball bearing-stator coupling system dynamic model is established. In the model, the rotor mass unbalance and rubbing faults are included, and the nonlinear factors of ball bearing such as the clearance of bearing, nonlinear Hertzian contract force between balls and races, and the varying compliance vibration coming from the periodical variety of contact positions between balls and races are modeled. The numerical integral method is employed to obtain system’s responses, and the vibration amplitude-rotating speed curve, bifurcation plot, phase plane plot, shaft centre orbits, frequency spectrum and Poincare´ map are used to carry out the analysis of bifurcation and chaos motion, and the effects of rotational speed, rubbing stiffness, rotor eccentricity, bearing house-stator stiffness, and stator-foundation stiffness on dynamic responses are analyzed, and the non-linear dynamic characteristics of rotor-ball bearing-stator system under unbalance and rubbing coupling faults are discovered.

scholarly journals EQUILIBRIUM CONDITIONS IN BEACH WAVE INTERACTION

1972 ◽  
Vol 1 (13) ◽  
pp. 62 ◽  
Author(s):  
H. Raman
Keyword(s):  
Wave Interaction ◽  
Experimental Results ◽  
Laboratory Studies ◽  
Regular Waves ◽  
Equilibrium Conditions ◽  
Wave Characteristics ◽  
New Criterion ◽  
Constant Characteristics ◽  
Stable Points

Laboratory studies were conducted in an attempt to find out a relationship between beach and wave characteristics when equilibrium conditions are reached in beach wave interaction for the simple case of regular waves acting normal to the beach. Experimental results indicate the existence of stable points on beach profiles where the coordinates of the profile do not change with time when waves of constant characteristics act on the beach. Emperical relationship between the wave and beach properties are proposed. A new criterion for classification of beach profiles is indicated.

A harmonic drive model considering geometry and internal interaction

2016 ◽  
Vol 231 (4) ◽  
pp. 728-743 ◽  
Author(s):  
Chuang Zou ◽  
Tao Tao ◽  
Gedong Jiang ◽  
Xuesong Mei ◽  
Junhui Wu
Keyword(s):  
Ball Bearing ◽  
Experimental Results ◽  
Torsional Stiffness ◽  
Harmonic Drive ◽  
Low Velocity ◽  
New Model ◽  
Internal Interaction ◽  
Drive Systems ◽  
Assembly Error ◽  
Drive Model

A new harmonic drive model considering the geometry, internal interactions and assembly error of key parts is proposed in this paper. In this model, a single tooth pair is used to represent the transmission mechanism of harmonic drive. The meshing stiffness between the flexspline and the circular spline, the torsional stiffness of the flexspline cylinder, and the radial stiffness of the thin-walled ball bearing are included and formulated. The kinematic error is fitted using a low-velocity test, and its generating mechanism is analysed. The friction of the harmonic drive is formulated at the tooth meshing section and at the ball bearing, where its parameters are identified based on experimental results. Based on the new model, velocity step simulations are conducted. For comparison, velocity step experiments at eight different velocities from 60 to 3000 r/min are performed, and the simulation results are in good agreement with the experimental results. The new model reveals the dynamic behaviour of the harmonic drive system; therefore, it will be useful for the dynamic design and precision control of harmonic drive systems.

Carriage Drift in Linear-Guideway Type Roller Bearings

2015 ◽  
Vol 137 (2) ◽  
Author(s):  
Hiroyuki Ohta ◽  
Taiki Kato ◽  
Soichiro Kato ◽  
Hideyuki Tajimi
Keyword(s):  
Ball Bearing ◽  
Roller Bearing ◽  
Experimental Results ◽  
Ball Bearings ◽  
Roller Bearings ◽  
Angular Displacements ◽  
Return Process

This study deals with carriage drift (which is the differences of the carriage displacements or angular displacements at a certain position on a rail during a forward and return process) in linear-guideway type roller bearings. First, the displacements and angular displacements of the carriage of the “nonrecirculating” linear roller and ball bearings under a reciprocating operation were measured. The experimental results showed that carriage drift (in the horizontal, vertical, yaw, and pitch directions) occurred in the roller bearing and not in the ball bearing. Next, in relationship to roller skew, the generating mechanism of carriage drift in roller bearings was examined by a multibody analysis (MBA), then the generating mechanism of carriage drift was explained. Finally, to reduce carriage drift by restricting the roller skew, an antiskewing brace (ASB) was developed.

Nonlinear Numerical Prediction of Gas Foil Bearing Stability and Unbalanced Response

2008 ◽  
Vol 131 (1) ◽  
Author(s):  
Sébastien Le Lez ◽  
Mihaï Arghir ◽  
Jean Frêne
Keyword(s):  
Dry Friction ◽  
Stability Limit ◽  
Time Step ◽  
Structural Dynamic ◽  
Friction Forces ◽  
Foil Bearings ◽  
Mass Unbalance ◽  
Foil Bearing ◽  
Highly Nonlinear ◽  
The Stability

One of the main interests of gas foil bearings lies in their superior rotordynamic characteristics compared with conventional bearings. A numerical investigation on the stability limit and on the unbalanced response of foil bearings is presented in this paper. The main difficulty in modeling the dynamic behavior of such bearings comes from the dry friction that occurs within the foil structure. Indeed, dry friction is highly nonlinear and is strongly influenced by the dynamic amplitude of the pressure field. To deal with these nonlinearities, a structural dynamic model has been developed in a previous work. This model considers the entire corrugated foil and the interactions between the bumps by describing the foil bearing structure as a multiple degrees of freedom system. It allows the determination of the dynamic friction forces at the top and at the bottom of the bumps by simple integration of ordinary differential equations. The dynamic displacements of the entire corrugated sheet are then easily obtained at each time step. The coupling between this structural model and a gas bearing prediction code is presented in this paper and allows performing full nonlinear analyses of a complete foil bearing. The bearing stability is the first investigated problem. The results show that the structural deflection enhances the stability of compliant surface bearings compared with rigid ones. Moreover, when friction is introduced, a new level of stability is reached, revealing the importance of this dissipation mechanism. The second investigated problem is the unbalanced response of foil bearings. The shaft trajectories depict a nonlinear jump in the response of both rigid and foil bearings when the value of the unbalance increases. Again, it is evidenced that the foil bearing can support higher mass unbalance before this undesirable step occurs.

scholarly journals Constrained Balancing of Two Industrial Rotor Systems: Least Squares and Min-Max Approaches

2009 ◽  
Vol 16 (1) ◽  
pp. 1-12 ◽  
Author(s):  
Bin Huang ◽  
Daiki Fujimura ◽  
Paul Allaire ◽  
Zongli Lin ◽  
Guoxin Li
Keyword(s):  
Least Squares ◽  
High Speed ◽  
Least Squares Method ◽  
Weighted Least Squares ◽  
Rotor Systems ◽  
Weighted Least Squares Method ◽  
Mass Unbalance ◽  
Second Order Cone ◽  
Residual Response ◽  
Rotor Mass

Rotor vibrations caused by rotor mass unbalance distributions are a major source of maintenance problems in high-speed rotating machinery. Minimizing this vibration by balancing under practical constraints is quite important to industry. This paper considers balancing of two large industrial rotor systems by constrained least squares and min-max balancing methods. In current industrial practice, the weighted least squares method has been utilized to minimize rotor vibrations for many years. One of its disadvantages is that it cannot guarantee that the maximum value of vibration is below a specified value. To achieve better balancing performance, the min-max balancing method utilizing the Second Order Cone Programming (SOCP) with the maximum correction weight constraint, the maximum residual response constraint as well as the weight splitting constraint has been utilized for effective balancing. The min-max balancing method can guarantee a maximum residual vibration value below an optimum value and is shown by simulation to significantly outperform the weighted least squares method.

Analysis of driveline loads in an automotive powertrain with multiple Cardan joints

2000 ◽  
Vol 214 (5) ◽  
pp. 509-522 ◽  
Author(s):  
V Krishna ◽  
N. G. Naganathan ◽  
R Phadnis ◽  
R. V. Dukkipati
Keyword(s):  
Time Domain Analysis ◽  
Angular Speed ◽  
Output Shaft ◽  
Equilibrium Analysis ◽  
Equilibrium Conditions ◽  
Angular Rotation ◽  
General Behaviour ◽  
Numerical Example ◽  
Contact Points ◽  
Automotive Powertrain

A general equilibrium analysis of automotive drivelines with multiple universal joints and numerous supporting conditions is presented. For the analysis, components of the driveline in terms of their angular rotation, angular velocity and acceleration are defined. Using kinematic conditions and a known torque and speed, the angular speed of the axle output shaft and all intermediate shafts and forces at contact points are computed using software developed to perform the analysis. To perform a time domain analysis, the quasi-static equilibrium conditions are imposed on the system at an instant. The instantaneous behaviour of the system is determined as a function of the transmission output shaft rotation. Finally, a numerical example is provided to illustrate the analysis. The results of the numerical example are plotted with respect to time. The general behaviour of the forces is found to be oscillatory and harmonic in nature.

Sign in / Sign up

Export Citation Format

Share Document