Dynamic Analysis of a Motorized Spindle With Externally Pressurized Air Bearings

2015 ◽  
Vol 137 (4) ◽  
Author(s):  
Chundong Xu ◽  
Shuyun Jiang
Keyword(s):  
Dynamic Characteristics ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Forced Response ◽  
Air Bearings ◽  
Motorized Spindle ◽  
Static And Dynamic Characteristics ◽  
Rotating Speed ◽  
Rotor Bearing ◽  
Bearing System

The purpose of this paper is to investigate the dynamic characteristics of a motorized spindle with externally pressurized air bearings. The externally pressurized air bearings consist of a journal bearing and a double pad thrust bearing with orifice restrictors. The equations of motion for the rotor-bearing system are established considering five degrees-of-freedom (DOF). The perturbation method and the finite difference method are introduced to calculate the static and dynamic characteristics of the air bearings; and the effects of the rotating speed and tilt angle of the rotor on the dynamic characteristics of the air bearings are analyzed. With the dynamic coefficients of the air bearings and the 5DOF rotor-dynamic model obtained, the stability, the unbalance response, and the forced response of the rotor-bearing system are investigated. Finally, the static and dynamic characteristics of the spindle are verified by an experimental study.

scholarly journals Nonlinear Dynamic Characteristics of Marine Rotor-Bearing System under Heaving Motion

2019 ◽  
Vol 2019 ◽  
pp. 1-16 ◽  
Author(s):  
Yongchao Han ◽  
Ming Li
Keyword(s):  
Dynamic Characteristics ◽  
Nonlinear Dynamic ◽  
Dynamic Performance ◽  
Chaotic Oscillation ◽  
Mathematic Model ◽  
Rotating Speed ◽  
Period 2 ◽  
Rotor Bearing ◽  
Motion Period ◽  
Bearing System

In this paper, the influence of the heaving motion on the nonlinear dynamic behavior of the rotor-bearing system is considered. First, a mathematic model of the marine rotor-bearing system is developed on the short bearing theory in the noninertial reference system, in which the heaving motion is taken into account. Then its dynamic characteristics are analyzed based on the numerical integration method, such as the bifurcation diagram, the largest Lyapunov exponents (LLE), the steady-state response, and the rotor orbit and its Poincaré map. The results indicate that heaving motion has a great effect on the dynamics of the rotor system, which exhibits a period 1 motion at low rotating speed, with the increase of the rotating speed, the phenomena of the quasiperiodic, period 2, and double Hopf bifurcations appear. Its dynamic performance presents a period 1 motion, period 2, quasiperiodic, and chaotic oscillation.

Stability Analysis of a Whirling Rigid Rotor Supported by FDBs Considering Five Degrees of Freedom of a General Rotor-Bearing System

2014 ◽  
Author(s):  
M. H. Lee ◽  
J. H. Lee ◽  
G. H. Jang
Keyword(s):  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Time Varying ◽  
Algebraic Equations ◽  
Dynamic Coefficients ◽  
Mass Unbalance ◽  
Whirling Motion ◽  
Rotor Bearing ◽  
The Stability ◽  
Bearing System

A rotor supported by fluid dynamic bearings (FDBs) has a whirling motion by centrifugal force due to the mass unbalance or by the flexibility of shaft. This whirling motion also generates periodic time-varying oil-film reaction and dynamic coefficients even in case of the stationary grooved FDBs. This paper proposes a method to determine the stability of a whirling rotor supported by stationary grooved FDBs considering five degrees of freedom of a general rotor-bearing system. Dynamic coefficients are calculated by using the finite element method and the perturbation method, and they are represented as periodic harmonic functions by considering whirling motion. Because of the periodic time-varying dynamic coefficients, the equations of motion of the rotor supported by FDBs can be represented as a parametrically excited system. The solution of the equations of motion can be assumed as the Fourier series so that the equations of motion can be rewritten as simultaneous algebraic equations with respect to the Fourier coefficients. Hill’s infinite determinant is calculated by using these algebraic equations in order to determine the stability. The stability of the FDBs decreases with the increase of rotational speed. The stability of the FDBs increases with the increase of whirl radius, because the average and variation of Cxx increase faster than those of Kxx. The proposed method is verified by solving the equations of motion by using the forth Runge-Kutta method to determine the convergence and divergence of whirl radius.

Effects of Shaft Shape Errors on the Dynamic Characteristics of a Rotor-Bearing System

2019 ◽  
Vol 141 (10) ◽  
Author(s):  
Fangxu Sun ◽  
Xianbiao Zhang ◽  
Xing Wang ◽  
Zhenzhong Su ◽  
Dong Wang
Keyword(s):  
Dynamic Characteristics ◽  
Computing Time ◽  
Quantitative Relationship ◽  
System Stability ◽  
Rotating Speed ◽  
Oil Whip ◽  
Rotor Bearing ◽  
Shape Errors ◽  
Reaction Forces ◽  
Bearing System

Effects of shaft shape errors are studied on dynamic characteristics of a rotor-bearing system. Stability characteristics of the cylindrical journal bearing are studied. It is shown that the rotating speed at which the oil whip occurs increases when the shape errors exit. And, there is a threshold speed of the bearing with shaft shape errors; before the speed is increased to the threshold, orbits of the center of the journal decrease, and when the speed exceeds the threshold, the orbits increase dramatically and oil whip appears. Furthermore, the quantitative relationship between shaft shape errors and bearing reaction forces of the rotor-bearing system is obtained, which is verified by experiments using rotors with different machining precisions. In order to reduce computing time, variational principle is applied when solving Reynolds’ equation.

Theoretical Prediction of Journal Center Motion Trajectory

1976 ◽  
Vol 98 (4) ◽  
pp. 620-628 ◽  
Author(s):  
D. V. Singh ◽  
R. Sinhasan ◽  
S. P. Tayal
Keyword(s):  
Theoretical Prediction ◽  
Dynamic Characteristics ◽  
Journal Bearing ◽  
Equations Of Motion ◽  
Motion Trajectory ◽  
Rotor Bearing ◽  
The Stability ◽  
Insight Into ◽  
Bearing System

By discretizing time and numerically integrating the equations of motion either for the linearized or the nonlinear journal bearing system, the locus of journal center can be predicted in the wake of a disturbance which upsets the equilibrium. From this locus, not only the stability of the system can be readily checked but also a greater insight into the dynamic characteristics of the rotor bearing systems can be obtained. Systems of solid bearings and porous bearings with journal bearing axes parallel as well as skewed have been studied.

scholarly journals Effect of preload on the dynamic characteristics of ceramic bearings based on a dynamic thermal coupling model

2020 ◽  
Vol 12 (1) ◽  
pp. 168781402090385
Author(s):  
Ke Zhang ◽  
Zinan Wang ◽  
Xiaotian Bai ◽  
Huaitao Shi ◽  
Qi Wang
Keyword(s):  
Dynamic Characteristics ◽  
High Speed ◽  
Thermal Deformation ◽  
Coupling Model ◽  
Transfer Model ◽  
Thermal Coupling ◽  
Motorized Spindle ◽  
Rotating Speed ◽  
Spindle Bearing ◽  
Bearing System

Ceramic bearings have a good dynamic output performance under an ultra-high, ultra-low temperature due to their small deformation property. Based on the Harris and Palmgren empirical equation, this article establishes the thermal transfer model of a ceramic motorized spindle. The thermal deformation of a ceramic angular contact ball bearing is calculated. A dynamic and thermal coupling model of the ceramic motorized spindle is built using the Hertz contact theory, which can determine the optimal preload force under different rotating speed conditions. The influence of different temperatures, preload, and rotation speeds on the bearing vibration characteristics was studied. The accuracy of the dynamic and thermal coupling model was verified by the motorized spindle experimental platform. The results show that the thermal deformation of the bearing is an important influencing factor for the output of the dynamic characteristics. Considering the thermal displacement of the bearing, the simulation accuracy of the ceramic motorized spindle-bearing system is in good agreement with the experimental results. By adjusting the bearing preload, the parameters of the rotating speed can effectively reduce the temperature rise and suppress the vibration. The spindle-bearing system model provides a theoretical basis for the dynamic development of a high-speed ceramic bearing.

scholarly journals Nonlinear Behavior of a Magnetic Bearing System

1995 ◽  
Vol 117 (3) ◽  
pp. 582-588 ◽  
Author(s):  
L. N. Virgin ◽  
T. F. Walsh ◽  
J. D. Knight
Keyword(s):  
Degrees Of Freedom ◽  
Initial Conditions ◽  
Nonlinear Behavior ◽  
Analytical Techniques ◽  
Magnetic Bearing ◽  
Forced Response ◽  
The Mathematical Model ◽  
Two Degree Of Freedom ◽  
Sensitivity To Initial Conditions ◽  
Bearing System

This paper describes the results of a study into the dynamic behavior of a magnetic bearing system. The research focuses attention on the influence of nonlinearities on the forced response of a two-degree-of-freedom rotating mass suspended by magnetic bearings and subject to rotating unbalance and feedback control. Geometric coupling between the degrees of freedom leads to a pair of nonlinear ordinary differential equations, which are then solved using both numerical simulation and approximate analytical techniques. The system exhibits a variety of interesting and somewhat unexpected phenomena including various amplitude driven bifurcational events, sensitivity to initial conditions, and the complete loss of stability associated with the escape from the potential well in which the system can be thought to be oscillating. An approximate criterion to avoid this last possibility is developed based on concepts of limiting the response of the system. The present paper may be considered as an extension to an earlier study by the same authors, which described the practical context of the work, free vibration, control aspects, and derivation of the mathematical model.

Dynamic analysis of a helical geared rotor-bearing system with composite rotating shafts

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Ying-Chung Chen ◽  
Xu Feng Cheng ◽  
Siu-Tong Choi
Keyword(s):  
Composite Material ◽  
Dynamic Analysis ◽  
Dynamic Characteristics ◽  
Mesh Stiffness ◽  
Content Type ◽  
Gear Mesh ◽  
Rotor Bearing ◽  
Rotating Shafts ◽  
Gear Mesh Stiffness ◽  
Bearing System

Purpose This study aims to study the dynamic characteristics of a helical geared rotor-bearing system with composite material rotating shafts. Design/methodology/approach A finite element model of a helical geared rotor-bearing system with composite material rotating shafts is developed, in which the rotating shafts of the system are composed of composite material and modeled as Timoshenko beam; a rigid mass is used to represent the gear and their gyroscopic effect is taken into account; bearings are modeled as linear spring-damper; and the equations of motion are obtained by applying Lagrange’s equation. Natural frequencies, mode description, lateral responses, axial responses, lamination angles, lamination numbers, gear mesh stiffness and bearing damping coefficients are investigated. Findings The desired mechanical properties could be constructed using different lamination numbers and fiber included angles by composite rotating shafts. The frequency of the lateral module decreases as the included angle of the fibers and the principal shaft of the composite material rotating shaft increase. Because of the gear mesh stiffness increase, the resonance frequency of the coupling module of the system decreases, the lateral module is not influenced and the steady-state response decreases. The amplitude of the steady-state lateral and axial responses gradually decreases as the bearing damping coefficient increases. Practical implications The model of a helical geared rotor-bearing system with composite material rotating shafts is established in this paper. The dynamic characteristics of a helical geared rotor-bearing system with composite rotating shafts are investigated. The numerical results of this study can be used as a reference for subsequent personnel research. Originality/value The dynamic characteristics of the geared rotor-bearing system had been reported in some literature. However, the dynamic analysis of a helical geared rotor-bearing system with composite material rotating shafts is still rarely investigated. This paper shows some novel results of lateral and axial response results obtained by different lamination angles and different lamination numbers. In the future, it makes valuable contributions for further development of dynamic analysis of a helical geared rotor-bearing system with composite material rotating shafts.

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