scholarly journals Time-Varying Dynamic Analysis of a Helical-Geared Rotor-Bearing System with Three-Dimensional Motion Due to Shaft Deformation

2020 ◽  
Vol 10 (4) ◽  
pp. 1542
Author(s):  
Ying-Chung Chen
Keyword(s):  
Equations Of Motion ◽  
Three Dimensional ◽  
Helix Angle ◽  
Dynamic Responses ◽  
Time Varying ◽  
Contact Ratio ◽  
Rotating Shaft ◽  
Rotor Bearing ◽  
Shaft Deformation ◽  
Bearing System

The rotordynamics of a helical-geared rotor-bearing system were investigated. A new dynamic model for a helical-geared rotor-bearing system, which takes into account three-dimensional (3-D) motion due to rotating shaft deformation, was proposed. The proposed model considers the time-varying effect, which in other models, is considered constant. The system equations of motion were obtained by applying Lagrange’s equation, and the dynamic responses were computed by the fourth-order Runge–Kutta method. The time-varying dynamic responses of the helix angle, transverse pressure angle, gear pair center distance, and total contact ratio were investigated. The numerical results show that the time-varying effect is an important factor in gear vibration analysis and cannot be neglected when the helical geared rotor-bearing system has a lower stiffness.

scholarly journals Time-varying dynamic analysis for a helical gear pair system with three-dimensional motion due to bearing deformation

2020 ◽  
Vol 12 (5) ◽  
pp. 168781402091812
Author(s):  
Ying-Chung Chen
Keyword(s):  
Three Dimensional ◽  
Helix Angle ◽  
Helical Gear ◽  
Dynamic Responses ◽  
Time Varying ◽  
Gear Pair ◽  
Contact Ratio ◽  
Transverse Pressure ◽  
Helical Gear Pair ◽  
Center Distance

The dynamic response of a helical gear pair system is investigated. A new dynamic model for a helical gear pair system, considering three-dimensional motion due to bearing deformation, is proposed. The proposed model considers the helix angle, gear pair center distance, transverse pressure angle, and the contact ratio as time-dependent variables, which are considered as constants in other models. In fact, three-dimensional motion due to bearing deformation will lead to the changes in a series of dynamic responses. The system equations of motion were obtained by applying Lagrange’s equation and the dynamic responses are computed by the fourth-order Runge–Kutta method. The time-varying dynamic displacements, helix angle, gear pair center distance, transverse pressure angle, and the contact ratio are investigated with bearing deformation, different radial bear stiffness, different axial bear stiffness, and gear eccentricity. The results show that, due to the time-varying effect, this new helical gear pair model provides more accurate dynamic responses than those previous models which are considered as constant. In the future, this study can provide some useful information for the time-varying dynamic design of a helical gear pair system.

Dynamic Analysis of a Spur Geared Rotor-Bearing System with Nonlinear Gear Mesh Stiffness

2014 ◽  
Vol 945-949 ◽  
pp. 853-861 ◽  
Author(s):  
Ying Chung Chen ◽  
Chung Hao Kang ◽  
Siu Tong Choi
Keyword(s):  
Dynamic Analysis ◽  
Equations Of Motion ◽  
Element Model ◽  
Dynamic Responses ◽  
Mesh Stiffness ◽  
Gear Mesh ◽  
Lagrange’S Equation ◽  
Rotor Bearing ◽  
Gear Mesh Stiffness ◽  
Bearing System

The gear mesh stiffnesses have been regarded as constants in most previous models of geared rotor-bearing systems. In this paper, a dynamic analysis of a spur geared rotor-bearing system with nonlinear gear mesh stiffness is presented. The nonlinear gear mesh stiffness is accounted for by bending, fillet-foundation and contact deflections of gear teeth. A finite element model of the geared rotor-bearing system is developed, the equations of motion are obtained by applying Lagrange’s equation, and the dynamic responses are computed by using the fourth-order Runge-Kutta numerical method. Numerical results indicate that the proposed gear mesh stiffness provides a realistic dynamic response for spur geared rotor-bearing system.

Dynamic Analysis of a Geared Rotor-Bearing System with Time-Varying Gear Mesh Stiffness and Pressure Angle

2013 ◽  
Vol 284-287 ◽  
pp. 461-467
Author(s):  
Ying Chung Chen ◽  
Chung Hao Kang ◽  
Siu Tong Choi
Keyword(s):  
Dynamic Analysis ◽  
Dynamic Responses ◽  
Time Varying ◽  
Mesh Stiffness ◽  
Gear Mesh ◽  
Pressure Angle ◽  
Proposed Model ◽  
Rotor Bearing ◽  
Gear Mesh Stiffness ◽  
Bearing System

The dynamic analysis of a geared rotor-bearing system with time-varying gear mesh stiffness and pressure angle is presented in this paper. Although there are analyses for both of the gear and rotor-bearing system dynamics, the coupling effect of the time-varying mesh and geared rotor-bearing system is deficient. Therefore, the pressure angle and contact ratio of the geared rotor-bearing system are treated as time-varying variables in the proposed model while they were considered as constant in previous models. The gear mesh stiffness is varied with different contact ratios of the gear pair in the meshing process. The nonlinear equations of motion for the geared rotor-bearing system are obtained by applying Lagrange’s equation and the dynamic responses are computed by using the Runge-Kutta numerical method. Numerical results of this study indicated that the proposed model provides realistic dynamic response of a geared rotor-bearing system.

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.

Analysis of an Accelerating Rotor-Bearing System With Flexible Damped Supports

1998 ◽  
Author(s):  
Euro L. Casanova ◽  
Luis U. Medina
Keyword(s):  
Steady State ◽  
Numerical Integration ◽  
Equations Of Motion ◽  
Peak Amplitude ◽  
Graphical Form ◽  
Jeffcott Rotor ◽  
Rotor Bearing ◽  
Flexible Supports ◽  
Steady State Predictions ◽  
Bearing System

This paper deals with the dynamics of an accelerating unbalanced Jeffcott rotor-bearing system mounted on damped, flexible supports. The general equations of motion for such a system are presented and discussed. The rotor response was predicted, via numerical integration, for various cases in runup and rundown conditions and presented in graphical form. The effects of acceleration on the rotor peak amplitude and the speed at which the peak occurs is discussed and compared to steady state predictions.

Nonlinear Vibration Signature Analysis of a High Speed Rotor Bearing System Due to Race Imperfection

2011 ◽  
Vol 7 (1) ◽  
Author(s):  
P. K. Kankar ◽  
Satish C. Sharma ◽  
S. P. Harsha
Keyword(s):  
High Speed ◽  
Nonlinear Differential Equations ◽  
Mathematical Formulation ◽  
Nonlinear Damping ◽  
Dynamic Responses ◽  
Fast Fourier Transformation ◽  
Surface Waviness ◽  
Contact Points ◽  
Rotor Bearing ◽  
Bearing System

In this paper the nonlinear dynamic responses of a rigid rotor supported by ball bearings due to surface waviness of bearing races are analyzed. A mathematical formulation has been derived with consideration of the nonlinear springs and nonlinear damping at the contact points of rolling elements and races, whose stiffnesses are obtained by using Hertzian elastic contact deformation theory. The numerical integration technique Newmark-β with the Newton–Raphson method is used to solve the nonlinear differential equations, iteratively. The effect of bearing running surface waviness on the nonlinear vibrations of rotor bearing system is investigated. The results are mainly presented in time and frequency domains are shown in time-displacement, fast Fourier transformation, and Poincaré maps. The results predict discrete spectrum with specific frequency components for each order of waviness at the inner and outer races, also the excited frequency and waviness order relationships have been set up to prognosis the race defect on these bearing components. Numerical results obtained from the simulation are validated with respect to those of prior researchers.

Coupled Lateral and Torsional Nonlinear Transient Rotor–Bearing System Analysis With Applications

2015 ◽  
Vol 137 (9) ◽  
Author(s):  
Jianming Cao ◽  
Paul Allaire ◽  
Timothy Dimond
Keyword(s):  
Rotational Speed ◽  
System Analysis ◽  
Equations Of Motion ◽  
Squeeze Film ◽  
Rotor Bearing ◽  
Nonlinear Transient ◽  
Gyroscopic Effects ◽  
Nonlinear Equations Of Motion ◽  
Torsional Analysis ◽  
Bearing System

This paper provides a time transient method for solving coupled lateral and torsional analysis of a flexible rotor–bearing system including gyroscopic effects, nonlinear short journal bearings, nonlinear short squeeze film dampers (SFDs), and external nonlinear forces/torques. The rotor is modeled as linear, and the supporting components, including bearings and dampers, are modeled as nonlinear. An implicit Runge–Kutta method is developed to solve the nonlinear equations of motion with nonconstant operating speed since the unbalance force and the gyroscopic effect are related to both the rotational speed and the acceleration. The developed method is compared with a previous torsional analysis first to verify the nonlinear transient solver. Then the coupled lateral and torsional analysis of an example flexible three-disk rotor, perhaps representing a compressor, with nonlinear bearings and nonlinear dampers driven by a synchronous motor is approached. The acceleration effects on lateral and torsional amplitudes of vibration are presented in the analysis. The developed method can be used to study the rotor motion with nonconstant rotational speed such as during startup, shutdown, going through critical speeds, blade loss force, or other sudden loading.

Nonlinear Dynamics Characteristic of Rotor-Bearing System by a Finite Element Model

2009 ◽  
Author(s):  
Chaofeng Li ◽  
Zhaohui Ren ◽  
Xiaopeng Li ◽  
Bangchun Wen
Keyword(s):  
Nonlinear Dynamic ◽  
Discrete Model ◽  
Element Model ◽  
Dynamic Responses ◽  
Runge Kutta Method ◽  
Significant Difference ◽  
Rotor Bearing ◽  
Comparison Of The Results ◽  
Bearing System ◽  
The Continuum

The nonlinear dynamic behavior of a rotor-bearing system is analyzed with its continuum model based on the analysis of the discrete model, with considering some other important influencing factors besides the nonlinear factors of the bearing, such as, the effect of inertia distribution and shear, transverse-torsion, structural geometric parameters of the system, which make the description of the system more embodiment and avoid the casualness of selection of system parameters. The dynamic responses of the continuum system and discrete system in the same unbalance condition are approached by the Runge-Kutta method and Newmark-β method. With the comparison of the results, significant difference about the dynamic characteristics is found with the addition of the considered factors. It is suggested that the substitution of discrete model by the continuum ones can get more accurate and abundant results. Furthermore, these results can provide more accurate verification and reference for the experiment and nonlinear dynamic design of the more complicated rotor system.

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