Nonlinear dynamic response analysis on gear-rotor-bearing transmission system

2016 ◽  
Vol 24 (9) ◽  
pp. 1632-1651 ◽  
Author(s):  
Shihua Zhou ◽  
Guiqiu Song ◽  
Mengnan Sun ◽  
Zhaohui Ren
Keyword(s):  
Friction Coefficient ◽  
Friction Force ◽  
Nonlinear Dynamic ◽  
Nonlinear Differential Equations ◽  
Transmission System ◽  
Dynamic Responses ◽  
Response Analysis ◽  
Light Load ◽  
Rotor Bearing ◽  
The Mean

A coupled lateral-torsional nonlinear dynamic model with 16-degree-of-freedom (16-DOF) of gear-rotor-bearing transmission system (GRBTS) is developed after comprehensive considering the nonlinear features associated with time-varying meshing stiffness, backlash, transmission error, friction force, input/output load, gravity and gear eccentricity. Based on the nonlinear differential equations, the coupled multi-body dynamic responses of the GRBTS are demonstrated using the Runge-Kutta numerical method, and the effects of friction coefficient and mean load on the dynamic characteristics are investigated. The results show that the friction force could enlarge the vibration amplitude and affect the low frequency components seriously. The mean load excitation has a complicated influence on the coupled GRBTS, and the torsional vibration is the dominate response. Whereas the mean load excitation has a certain extent vibration suppression, and light load and heavy load could no longer effectively control the nonlinear vibration of the GRBTS. With the increasing of rotational speed, the friction coefficient and mean load ranges of the chaotic behavior widen and the chaotic characteristics strengthens. It is shown that small parameter random perturbation might be propagated in the vibration system and lead to relatively large vibration of the system. The contribution to provide a reference for the design and study of gear system.

Influences of Wind Barriers on the Train Running Safety on a Highway-Railway One-Story Bridge

2021 ◽  
pp. 2140009
Author(s):  
Ye Liu ◽  
Yan Han ◽  
Peng Hu ◽  
C. S. Cai ◽  
Xuhui He
Keyword(s):  
Dynamic Responses ◽  
Response Analysis ◽  
Train Track ◽  
Wheel Load ◽  
Wind Barrier ◽  
The Mean ◽  
Wind Pressures ◽  
Track Bridge ◽  
Fluctuating Wind ◽  
Bridge System

In this study, the influences of wind barriers on the aerodynamic characteristics of trains (e.g. a CRH2 train) on a highway-railway one-story bridge were investigated by using wind pressure measurement tests, and a reduction factor of overturning moment coefficients was analyzed for trains under wind barriers. Subsequently, based on a joint simulation employing SIMPACK and ANSYS, a wind–train–track–bridge system coupled vibration model was established, and the safety and comfort indexes of trains on the bridge were studied under different wind barrier parameters. The results show that the mean wind pressures and fluctuating wind pressures on the trains’ surface decrease generally if wind barriers are used. As a result, the dynamic responses of the trains also decrease in the whole process of crossing the bridge. Of particular note, the rate of the wheel load reductions and lateral wheel-axle forces can change from unsafe states to relative safe states due to the wind barriers. The influence of the porosity of the wind barriers on the mean wind pressures and fluctuating wind pressures on the windward sides and near the top corner surfaces of the trains are significantly greater than the influence from the height of the wind barriers. Within a certain range, decreasing the wind barrier porosities and increasing the wind barrier heights will significantly reduce the safety and comfort index values of trains on the bridge. It is found that when the porosity of the wind barrier is 40%, the optimal height of the wind barrier is determined as approximately 3.5[Formula: see text]m. At this height, the trains on the bridges are safer and run more smoothly and comfortably. Besides, through the dynamic response analysis of the wind–train–track–bridge system, it is found that the installation of wind barriers in cases with high wind speeds (30[Formula: see text]m/s) may have an adverse effect on the vertical vibration of the train–track–bridge system.

Friction Characteristics and Adhesion Force Under Low Normal Load

1995 ◽  
Vol 117 (4) ◽  
pp. 569-574 ◽  
Author(s):  
Yasuhisa Ando ◽  
Yuichi Ishikawa ◽  
Tokio Kitahara
Keyword(s):  
Friction Coefficient ◽  
Friction Force ◽  
Adhesion Force ◽  
Normal Load ◽  
Adhesion Forces ◽  
Test Pieces ◽  
Before And After ◽  
Constant Normal Load ◽  
The Mean ◽  
Steel Balls

The friction coefficient and adhesion force between steel balls and flat test pieces were measured during friction under low normal load in order to examine the tribological characteristics. First, the friction coefficients were measured under a constant normal load of 0.8 to 2350 μN, and the adhesion forces were measured before and after each friction. The result showed that the friction coefficient was highest at low normal loads, while the friction force divided by the sum of the normal load and the mean adhesion force was almost constant over the whole range of loads. Second, when the normal load was reduced gradually during friction, friction still acted when the normal load became negative and a pulling off force was applied to the surface. Thus an adhesion force acts during friction and this adhesion force affects the friction force in the same way as the normal load.

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.

Perturbation Analysis of Texture Effects on Lubricated Devices

2005 ◽  
Author(s):  
Gustavo C. Buscaglia ◽  
Mohammed Jai ◽  
Sorin Ciuperca
Keyword(s):  
Friction Coefficient ◽  
Friction Force ◽  
Perturbation Analysis ◽  
Mathematical Analysis ◽  
Load Capacity ◽  
Second Order ◽  
Numerical Investigations ◽  
First Order ◽  
The Mean

Given a bearing of some specified shape, what is the effect of texturing its surfaces uniformly? Experimental and numerical investigations on this question have recently been pursued, which we complement here with a mathematical analysis. Assuming the texture length to be much smaller than the bearing’s length, we combine homogenization techniques with perturbation analysis. This allows us to consider arbitrary, 2D texture shapes. The results show that both the load capacity and the friction force depend, to first order in the amplitude, just on the mean depth/height of the texture. The dependence of the friction coefficient is thus of second order.

Effects of gearbox housing flexibility on dynamic characteristics of gear transmission system

2020 ◽  
pp. 107754632095373
Author(s):  
Xiannian Kong ◽  
Jinyuan Tang ◽  
Chen Siyu ◽  
Zehua Hu
Keyword(s):  
Dynamic Analysis ◽  
Natural Frequencies ◽  
Lightweight Design ◽  
Transmission System ◽  
Structure Design ◽  
Gear Transmission ◽  
Dynamic Responses ◽  
Dynamic Behaviors ◽  
Gear Transmission System ◽  
Rotor Bearing

The lightweight design of the gear system is the current tendency. The gearbox housing is modeled as a rigid body and is neglected in the gear dynamic analysis. It is of great significance to introduce the gearbox housing flexibility into the dynamic analysis and analyze the influence of the gearbox housing flexibility on the dynamic behaviors of the gear transmission system, as this can provide important instructions for the lightweight structure design of the housing. The gear–rotor–bearing model and the gear–rotor–bearing–housing model are established by the finite element node method. A Timoshenko beam element is used to represent the shafts. To illustrate the housing effect, two kinds of housing model are established: one tends to be rigid and the other to be flexible and lighter. The housings are simplified as a super element obtained by the dynamic substructure method. Natural frequencies and dynamic responses are illustrated to indicate the effects of housing flexibility. Comparisons of numerical results show that the rigid housing can be neglected for its little effect on the dynamic analysis. The flexibility of the housing slightly reduces the natural frequencies of the gear transmission system, and the maximum reduction is 6.05%. Meanwhile, the amplitudes of the first two resonance peaks of the dynamic transmission error decrease by 9.5% and 5.05%. Besides, more response peaks emerge at higher speeds when the flexibility of housing increases. The complete phenomena of dynamic behaviors of the gear transmission system can be obtained by considering the housing flexibility.

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.

A Dynamic Friction Model for Unlubricated Rough Planar Surfaces

2003 ◽  
Vol 125 (4) ◽  
pp. 788-796 ◽  
Author(s):  
Xi Shi ◽  
Andreas A. Polycarpou
Keyword(s):  
Friction Coefficient ◽  
Friction Force ◽  
Harmonic Excitation ◽  
Published Data ◽  
Dynamic Friction ◽  
Time Varying ◽  
Friction Forces ◽  
Dynamic Friction Coefficient ◽  
Normal Separation ◽  
The Mean

Modeling dynamic or kinetic friction for realistic engineering surfaces continues to be a challenge, partly due to the coupling between system dynamics and interfacial forces. In this paper, a dynamic friction coefficient model for realistic rough surfaces under external normal vibrations is developed. From the system dynamic model, the instantaneous time varying normal separation at the interface is obtained under normal harmonic excitation. Subsequently, the instantaneous dynamic contact and tangential (friction) forces are calculated as a function of the instantaneous normal separation. The dynamic friction coefficient defined as the ratio of the time varying friction to the interfacial normal forces that explicitly includes interfacial damping, is also calculated. The results show that a mean increase in the instantaneous normal separation may or may not lead to a decrease of the mean friction force and the mean friction coefficient, which is supported by published data. For unlubricated elastic sliding contact conditions considered in this paper, the effect of damping on the dynamic friction coefficient is found to be negligible, whereas loss of contact causes significant apparent dynamic friction force and dynamic friction coefficient reductions. Several different interpretations of the time varying dynamic friction coefficient are presented and the implications of using a simple constant value to represent the time varying dynamic friction coefficient are discussed.

scholarly journals Nonlinear Torsional Dynamics of Star Gearing Transmission System of GTF Gearbox

2020 ◽  
Vol 2020 ◽  
pp. 1-15 ◽  
Author(s):  
Siyu Wang ◽  
Rupeng Zhu
Keyword(s):  
Nonlinear Dynamic ◽  
Damping Ratio ◽  
Global Bifurcation ◽  
Period Doubling ◽  
Transmission System ◽  
Dynamic Responses ◽  
Nonlinear Dynamic Model ◽  
Chaotic Motions ◽  
Meshing Stiffness ◽  
And Control

Considering time-varying meshing stiffness, comprehensive errors, and piecewise backlash nonlinearities of gear and spline, a torsional nonlinear dynamic model of star gear-rotor coupling transmission system of (Geared Turbofan Engine) GTF aeroengine is established. By using the Runge–Kutta numerical integration method, the dynamic responses are solved, analyzed, and illustrated with the bifurcation parameters including input rotational speed, gear backlash, damping ratio, and comprehensive meshing errors. The motions of the star gearing system and diverse nonlinear dynamic characteristics are identified through global bifurcation, FFT spectra, Poincaré map, and the phase diagram. The results reveal that the star gear-rotor system exhibits abundant torsional nonlinear behaviors, including multiperiodic, quasi-periodic, and chaotic motions. Furthermore, the roads to chaos via quasi-periodicity, period-doubling scenario, and mutation are demonstrated. These results provide an understanding of undesirable torsional dynamic motion for the GTF transmission system and provide a reference for the design and control of gear system.

Nonlinear Dynamics in the Estimation of Rotor-Bearing Dynamic Properties in Large Hydro-Units*

1999 ◽  
Author(s):  
X. Z. Zhang ◽  
B. G. Liu
Keyword(s):  
Nonlinear Dynamics ◽  
Nonlinear Dynamic ◽  
Natural Frequencies ◽  
Dynamic Properties ◽  
Dynamic Responses ◽  
Dynamic Loads ◽  
Nonlinear Dynamic Response ◽  
Rotor Bearing ◽  
Dynamic Eccentricity ◽  
Bearing System

Abstract This paper describes a method with which the nonlinear dynamic response and the natural features of rotor-bearing systems in large hydro-units can be estimated on a personal computer. The key step of this process is to estimate the dynamic eccentricity of the journal center in every guide bearing when the system is subjected to dynamic loads. As an example, the nonlinear dynamic responses, the natural frequencies and the critical speeds of the rotor-bearing system of a 240MW hydro-unit are calculated. The calculated dynamic responses agree well with the ones measured in the field.

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