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.

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.

Coupled Bending-Torsion Vibration of Geared Rotors

1995 ◽  
Author(s):  
J. S. Rao ◽  
J. R. Chang ◽  
T. N. Shiau
Keyword(s):  
Finite Element ◽  
Natural Frequencies ◽  
Element Model ◽  
Mode Shapes ◽  
Mesh Stiffness ◽  
Present Program ◽  
Gear Mesh ◽  
Pressure Angle ◽  
Torsion Vibration ◽  
Gear Mesh Stiffness

Abstract A general finite element model is presented for determining the coupled bending-torsion natural frequencies and mode shapes of geared rotors. Uncoupled bending and torsion frequencies are obtained for examples available in literature and the present program is verified against these. The effect of the gear box is considered to determine the coupled frequencies. Parameters studied include the pressure angle, gear mesh stiffness, and bearing properties. The gear pressure angle is shown to have no effect on the natural frequencies of rotors supported on isotropic bearing supports. Several case studies with bending-torsion coupling are considered and the results obtained are compared with those available in literature. The results of a general rotor system with 8lodes are also presented.

Multilevel Optimization of the Geared Rotor-Bearing System for Multi-Objectives With Critical Speed Constraints

2004 ◽  
Author(s):  
T. N. Shiau ◽  
J. R. Chang ◽  
W. B. Lu
Keyword(s):  
Critical Speed ◽  
Transmission Error ◽  
Mesh Stiffness ◽  
Error Response ◽  
Critical Speeds ◽  
Gear Mesh ◽  
Unbalance Response ◽  
Multilevel Algorithm ◽  
Gear Mesh Stiffness ◽  
Bearing System

This paper presents the multi-objective optimization of a geared rotor-bearing system with the critical speeds constraints by using an efficient multilevel algorithm. The weight of each rotor shaft, the unbalance response, and the response due to the transmission error are minimized simultaneously under the critical speed constraints. The design variables are the inner radii of the shaft, the stiffness of bearings, and the gear mesh stiffness. The finite element method (FEM) is employed to analyze the dynamic characteristics and the method of feasible direction (MFD) is applied in the optimization of the single objective stage. Based on the sensitivity analysis that gear mesh stiffness has almost no influences on the critical speeds of the uncoupled modes of two shafts, an efficient multilevel algorithm composed of system and subsystem levels is developed. In the cycle of iteration, the minimization of the shaft weight is performed in the subsystem level with the critical speed constraints of only uncoupled modes of two shafts and the unbalance response and the transmission error response are reduced in the system level with the critical speed constraints of only coupled modes. It is indicated from the numerical results that the shaft weight, the unbalance response, and the transmission error response via the multilevel technique (ML) are all reduced much more than those via the weighting method (WM) and the goal programming method (GPM).

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.

Dynamics of a Truck Gearbox

1992 ◽  
Author(s):  
J. Perret-Liaudet ◽  
J. Sabot
Keyword(s):  
Numerical Simulations ◽  
Dynamic Behaviour ◽  
Equations Of Motion ◽  
Transmission Error ◽  
Gear Transmission ◽  
The Finite Element Method ◽  
Mesh Stiffness ◽  
Gear Mesh ◽  
Static Transmission Error ◽  
Gear Mesh Stiffness

Abstract This work is concerned with numerous numerical simulations of the overall dynamic behaviour of a parallel helical gear transmission. These results are compared to vibratory measurements made with a simplified gearbox test rig. The dynamic modeling of the elastic components of the gear transmission (gears, shafts, bearings, housing) is realized using the finite element method. Fluctuated gear mesh stiffness is introduced owing to stiffness matrix which describes the elastic coupling between the pinion and the wheel. The kinematic transmission error is introduced as a vibratory excitation source. The equations of motion are established in a truncated modal base deduced from the average characteristics of the structure. A new computing method, called “Spectral Method”, is used for analytical study of a simplified gearbox whose housing is a simple rectangular plate. The numerical results allows us to conclude on the dominent phenomenon of the overall dynamic behaviour of the gear transmission. They exhibit in particular the main characteristics of the transfer between the static transmission error and the vibratory response of the gearbox. A series of vibration measurements made on a gearbox close to that used for the numerical simulations, has confirmed this characteristics.

Mesh stiffness modeling considering actual tooth profile geometry for a spur gear pair

2018 ◽  
Vol 19 (3) ◽  
pp. 306 ◽  
Author(s):  
Yong Yang ◽  
Jiaxu Wang ◽  
Qinghua Zhou ◽  
Yanyan Huang ◽  
Jinxuan Zhu ◽  
...  
Keyword(s):  
Gear Tooth ◽  
Analytical Description ◽  
Element Model ◽  
Spur Gear ◽  
Tooth Profile ◽  
Mesh Stiffness ◽  
Gear Mesh ◽  
Proposed Model ◽  
Tooth Stiffness ◽  
Gear Mesh Stiffness

Some tooth profile geometric features, such as root fillet area, flank modification and wear are of nonnegligible importance for gear mesh stiffness. However, due to complexity of analytical description, their influence on mesh stiffness was always ignored by existing research works. The present work derives analytical formulations for time-varying gear mesh stiffness by using parametric equations of flank profile. Tooth geometry formulas based upon a rack-type tool are derived following Litvin's vector approach. The root fillet area and tooth profile deviations can therefore be fully considered for spur gear tooth stiffness evaluation. The influence of gear fillet determined by tip fillet radius of the rack-type tool is quantified parametrically. The proposed model is validated to be effective by comparing with a finite element model. Further, the model is applied to investigate the stiffness variations produced by tooth addendum modification, tooth profile nonuniform wear and modification.

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.

Numerical Simulation of Nonlinear Spur Gear Dynamics

1999 ◽  
Author(s):  
Nagaraj K. Arakere ◽  
C. Nataraj
Keyword(s):  
High Speed ◽  
Equations Of Motion ◽  
Spur Gear ◽  
Journal Bearings ◽  
Accurate Estimation ◽  
Gear Pair ◽  
Mesh Stiffness ◽  
Gear Teeth ◽  
Gear Mesh ◽  
Gear Mesh Stiffness

Abstract An analytical investigation of the nonlinear dynamics of a high-speed spur-gear pair supported on journal bearings is presented. Dynamic tooth loads result from the interaction between periodic variation of gear mesh stiffness, involute tooth profile errors and gear rotor dynamics. Accurate estimation of dynamic tooth loads, as the gear teeth engage and disengage, is critical for fatigue life estimation. Load-deflection characteristics of a spur gear mesh and the periodically varying gear mesh stiffness is developed using a finite element model. Relative displacement between the gear teeth (transmission error) due to tooth deflection along the line of action is evaluated. The coupled torsional-lateral vibrations of a spur-gear pair supported on journal bearings is modeled as a six degree of freedom system. The time dependent radial and tangential forces acting on the gear shaft supported on journal bearings is evaluated. Short bearing theory is used for modeling the journal bearing dynamics. The resulting nonlinear equations of motion are numerically integrated to obtain gear and pinion whirl orbits due to unbalance excitation and dynamic tooth load variation. Dynamic tooth loads are compared with the mean load due to torque transmission.

Dynamic analysis of a helical gear reduction by experimental and numerical methods

2020 ◽  
Vol 68 (1) ◽  
pp. 48-58
Author(s):  
Chao Liu ◽  
Zongde Fang ◽  
Fang Guo ◽  
Long Xiang ◽  
Yabin Guan ◽  
...  
Keyword(s):  
Numerical Methods ◽  
Dynamic Analysis ◽  
Dynamic Behavior ◽  
Fourth Order ◽  
Numerical Models ◽  
Helical Gear ◽  
Operating Conditions ◽  
Dynamic Responses ◽  
Lumped Mass ◽  
Gear Mesh

Presented in this study is investigation of dynamic behavior of a helical gear reduction by experimental and numerical methods. A closed-loop test rig is designed to measure vibrations of the example system, and the basic principle as well as relevant signal processing method is introduced. A hybrid user-defined element model is established to predict relative vibration acceleration at the gear mesh in a direction normal to contact surfaces. The other two numerical models are also constructed by lumped mass method and contact FEM to compare with the previous model in terms of dynamic responses of the system. First, the experiment data demonstrate that the loaded transmission error calculated by LTCA method is generally acceptable and that the assumption ignoring the tooth backlash is valid under the conditions of large loads. Second, under the common operating conditions, the system vibrations obtained by the experimental and numerical methods primarily occur at the first fourth-order meshing frequencies and that the maximum vibration amplitude, for each method, appears on the fourth-order meshing frequency. Moreover, root-mean-square (RMS) value of the acceleration increases with the increasing loads. Finally, according to the comparison of the simulation results, the variation tendencies of the RMS value along with input rotational speed agree well and that the frequencies where the resonances occur keep coincident generally. With summaries of merit and demerit, application of each numerical method is suggested for dynamic analysis of cylindrical gear system, which aids designers for desirable dynamic behavior of the system and better solutions to engineering problems.

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