Nonlinear Dynamic of a Geared Rotor System With Nonlinear Oil Film Force and Nonlinear Mesh Force

2012 ◽  
Vol 134 (4) ◽  
Author(s):  
Yahui Cui ◽  
Zhansheng Liu ◽  
Yongliang Wang ◽  
Jianhuai Ye
Keyword(s):  
Numerical Integration ◽  
Dynamic Model ◽  
Rotational Speed ◽  
Nonlinear Dynamic ◽  
Journal Bearing ◽  
Rotational Frequency ◽  
Rotor System ◽  
Dynamic Responses ◽  
Oil Film ◽  
Gear Mesh

To investigate the effect of oil film force on a geared rotor system, a short journal bearing model was applied to represent nonlinear oil film force. A dynamic model of the geared rotor oil journal bearing system was presented. The nonlinear gear mesh force and nonlinear oil film force were considered in the model. The nonlinear dynamic responses of the system were investigated by numerical integration method. This article shows that when the rotational speed is relatively low, the vibration of the system is mainly affected by nonlinear mesh force. With the increase of rotational speed, the influence of nonlinear oil film force also increases gradually, and the subsynchronous forward precession phenomena appear. When the speed increases to a certain value, the amplitude of the subsynchronous forward precession exceeds the amplitude of the rotational frequency, and the nonlinear mesh force is greatly affected by the nonlinear oil film force. However, the linear oil film force does not affect the nonlinear mesh force. The subsynchronous forward precession is difficult to be predicted by linear oil film force which was previously applied. This experiment is performed to validate the correctness of the dynamic model presented, and the numerical integration results of low speeds are validated by the experimental data.

scholarly journals Rattle dynamics of noncircular face gear under multifrequency parametric excitation

2021 ◽  
Vol 12 (1) ◽  
pp. 361-373
Author(s):  
Dawei Liu ◽  
Zhenzhen Lv ◽  
Guohao Zhao
Keyword(s):  
Dynamic Model ◽  
Parametric Excitation ◽  
Nonlinear Dynamic ◽  
Velocity Ratio ◽  
Harmonic Balance Method ◽  
Transmission Error ◽  
Dynamic Responses ◽  
Discrete Fourier Transformation ◽  
Nonlinear Dynamic Model ◽  
Face Gear

Abstract. A noncircular face gear (NFG) conjugated with a pinion is a new type of face gear which can transmit variable velocity ratio and in which two time-varying excitations exist, namely the meshing stiffness excitation and instantaneous center excitation. Considering the tooth backlash, static transmission error and multifrequency parametric excitation, a nonlinear dynamic model of the NFG pair is presented. Based on the harmonic balance method and discrete Fourier transformation, a semi-analytic approach for the nonlinear dynamic model is given to analyze the dynamic behaviors of the NFG. Results demonstrate that, with increase in the eccentric ratio, input velocity and error amplitude, the NFG will undergo a non-rattle, unilateral rattle and bilateral rattle state in succession, and a jump phenomenon will appear in the dynamic responses when the rattle state of the gears is transformed from unilateral rattle to bilateral rattle.

Stability and Bifurcation of Nonlinear Bearing-Flexible Rotor System with a Single Disk

2010 ◽  
Vol 148-149 ◽  
pp. 141-146
Author(s):  
Di Hei ◽  
Yong Fang Zhang ◽  
Mei Ru Zheng ◽  
Liang Jia ◽  
Yan Jun Lu
Keyword(s):  
Nonlinear Dynamic ◽  
Degrees Of Freedom ◽  
Rotor System ◽  
Dynamic Responses ◽  
Flexible Rotor ◽  
Runge Kutta Method ◽  
Stability And Bifurcation ◽  
Single Disk ◽  
The Stability ◽  
Predictor Corrector

Dynamic model and equation of a nonlinear flexible rotor-bearing system are established based on rotor dynamics. A local iteration method consisting of improved Wilson-θ method, predictor-corrector mechanism and Newton-Raphson method is proposed to calculate nonlinear dynamic responses. By the proposed method, the iterations are only executed on nonlinear degrees of freedom. The proposed method has higher efficiency than Runge-Kutta method, so the proposed method improves calculation efficiency and saves computing cost greatly. Taking the system parameter ‘s’ of flexible rotor as the control parameter, nonlinear dynamic responses of rotor system are obtained by the proposed method. The stability and bifurcation type of periodic responses are determined by Floquet theory and a Poincaré map. The numerical results reveal periodic, quasi-periodic, period-5, jump solutions of rich and complex nonlinear behaviors of the system.

Nonlinear Dynamic Oil-Film Forces in Infinite-Short Journal Bearings

2011 ◽  
Author(s):  
Lihua Yang ◽  
Weimin Wang ◽  
Lie Yu
Keyword(s):  
Nonlinear Dynamic ◽  
Reynolds Equation ◽  
Journal Bearing ◽  
Analytic Solutions ◽  
Journal Bearings ◽  
Oil Film ◽  
Dynamic Coefficients ◽  
Representation Model ◽  
Linear And Nonlinear

In this paper, the analytic solutions of oil-film forces in infinite-short cylindrical journal bearing are calculated by solving its corresponding Reynolds equation. On this base, the linear and nonlinear dynamic coefficients of the bearing are predicted. By comparing the dynamic oil-film forces approximately represented by dynamic coefficients with the analytic solutions, the accuracy of this representation model is investigated. The results show that more orders of dynamic coefficients are included in representation model, the obtained approximate oil-film forces are more close to their analytic solutions. This can be a reference to illustrate the feasibility and applicability of representing oil-film forces by applying the dynamic coefficients of bearings.

scholarly journals Multibody Dynamic Analysis of a Wind Turbine Drivetrain in Consideration of the Shaft Bending Effect and a Variable Gear Mesh Including Eccentricity and Nacelle Movement

2021 ◽  
Vol 8 ◽  
Author(s):  
Yonghui Park ◽  
Hyunchul Park ◽  
Zhe Ma ◽  
Jikun You ◽  
Wei Shi
Keyword(s):  
Wind Turbine ◽  
Dynamic Model ◽  
Gear Tooth ◽  
Translational Motion ◽  
Three Dimensional ◽  
Contact Forces ◽  
Dynamic Responses ◽  
Renewable Energy Resources ◽  
Gear Mesh ◽  
Direct Numerical Integration

Due to the energy crisis and global warming issues, the wind energy is becoming one of the most attractive renewable energy resources in the world. The drivetrains in the wind turbine tend to fail more prematurely than those in any other applications. Gearbox is the subsystem that causes the most downtime for the wind turbines. In the previous research, only the torsional flexibility of the shaft was considered in the drivetrain model. However, because the shaft is longer than other parts, and components connected by the shaft affect each other via shaft bending, the flexibility of the shaft cannot be ignored. In this study, a spherical joint that consists of three rotational springs was used to define the shaft bending. This shaft bending will affect the drivetrain rotation, the translational motion and the gear mesh contact force. Additionally, the eccentricity and the nacelle movement are analyzed due to the coupled motion. In this paper, a mathematical model of the drivetrain is proposed, which is a three-dimensional dynamic model that includes flexible bearings, a gear mesh model, shaft flexibility, eccentricity, and nacelle movement. The equation of motion of the drivetrain is derived using Lagrange's equation. The governing equation is solved numerically via direct numerical integration. The dynamic responses of the system and contact forces between the gear tooth in the time and frequency domains are calculated numerically. The study shows that this dynamic model of the drivetrain will be highly useful for subsequent studies on the wind turbine condition monitoring.

Study on the Dynamic Response of an Unbalanced Rotor System Supported by Ball Bearings

2019 ◽  
Author(s):  
Bin Fang ◽  
Jinhua Zhang ◽  
Ke Yan ◽  
Jun Hong
Keyword(s):  
Dynamic Model ◽  
Ball Bearing ◽  
Great Influence ◽  
Rotor System ◽  
Dynamic Responses ◽  
Ball Bearings ◽  
Motion Patterns ◽  
Symmetric Rotor ◽  
Asymmetric Rotor ◽  
Restoring Forces

Abstract This paper proposed a new four-degree-of-freedom dynamic model of the bearing-rotor system based on ball bearing without Raceway Control Hypothesis, and both the inertia forces of balls and the tilting motions of rotor are fully considering in the calculation of restoring forces and moments of ball bearings. Then the dynamic model are solved by the fourth-step Runge-Kutta method, and the dynamic responses of rotor system including the displacement, velocity and center orbits are obtained, and the influences of rotating speeds, eccentricity and symmetry of rotor are studied and analyzed. The results show that both the varying compliance of ball bearing and rotor eccentric force have a great influence on the dynamic responses and motion patterns of bearing-rotor system, and the titling motion of bearing-rotor should be considered in the analysis of asymmetric rotor or the symmetric rotor under some specific conditions.

Analysis of aerostatic spindle radial vibration error based on microscale nonlinear dynamic characteristics

2019 ◽  
Vol 25 (14) ◽  
pp. 2043-2052 ◽  
Author(s):  
Dongju Chen ◽  
Na Li ◽  
Ri Pan ◽  
Jihong Han
Keyword(s):  
Dynamic Model ◽  
Nonlinear Dynamic ◽  
Degrees Of Freedom ◽  
Dynamic Stiffness ◽  
Prediction Method ◽  
Rotor System ◽  
Rotation Error ◽  
Spindle Rotation ◽  
Microscale Effect ◽  
Aerostatic Spindle

This paper presents a method of predicting the radial rotary error of an aerostatic spindle based on the microscale-effect to investigate the influence of gas film fluctuation on the rotation accuracy of the aerostatic spindle. First, the gas bearing of the spindle is simplified as a spring-damping system with two degrees of freedom perpendicular to each other. Additionally, the aerostatic spindle bearing-rotor system is established by considering the forced vibration and deflection vibration of the rotor. Subsequently, the microscale-effect is introduced into the dynamic model of the gas film flow, and the dynamic Reynolds equation of the gas film is established in the microscale. Moreover, the nonlinear dynamic stiffness and dynamic damping coefficient are obtained by the perturbation method. The nonlinear dynamic parameters in the microscale are introduced into the dynamic model of the bearing-rotor system and all the vibration errors are obtained. By comparison with the conventional case, it is found that the spindle gyration error increased and that the response delay occurred when the microscale-effect is considered. Moreover, the influence of the supply pressure and speed on the vibration of the spindle is also analyzed. An experiment measuring the spindle rotation error is carried out. The experimental results reveal that the prediction method of the nonlinear spindle rotation error in the microscale is more accurate, and that the errors are 5.8% and 9.6%.

Study on Subsynchronous Vibration With Tilting Pad Journal Bearing Under Starved Lubrication

2018 ◽  
Author(s):  
Rimpei Kawashita ◽  
Tadasuke Nishioka ◽  
Shimpei Yokoyama ◽  
Makoto Iwasaki ◽  
Shuichi Isayama ◽  
...  
Keyword(s):  
Flow Rate ◽  
Journal Bearing ◽  
Damping Ratio ◽  
Leading Edge ◽  
Rotor System ◽  
Experimental Results ◽  
Oil Film ◽  
Tilting Pad ◽  
Oil Flow ◽  
Starved Lubrication

Industrial machines such as gas and steam turbines require high efficiency and reliability. Direct lubricated bearings have been developed and installed to reduce mechanical losses. In recent years, it has been reported in the literature that subsynchronous vibration can occur to rotor shafts with direct lubricated tilting pad journal bearings under reduced oil flow rate conditions. In this study, a test rig with a 200 mm diameter and 3.5 meter long rotor supported by a direct lubricated tilting two pad journal bearing was constructed. The primary critical speed is 2100rpm and rotational speed is 3600rpm. The oil-starved area, the non-oil film layer region at the leading edge of the bearing pads, was measured by observing oil film pressure in the bearing clearance with pressure transducers on the rotor surface. A sine sweep excitation test was carried out by using an inertial shaker installed on the bearing housing and the damping ratio of the rotor system was measured. Measured data showed that a larger starved area at the leading edge of the bearing pads due to reduced oil feeding results in a smaller damping ratio, and an increase in the natural frequency of the rotor. Experimental results of two types of oil feeding nozzles were compared with respect to the correlation between starved area and damping ratio of the rotor system, and a relationship between oil flow rate and starved area was discussed. A method for modeling bearing coefficients under starved lubrication has been proposed based on thermo-hydrodynamic lubrication (THL) analysis. A numerical analysis of a finite element-transfer matrix model of the test rotor with the bearing coefficients calculated by the proposed method is carried out, and it is found that the analytical results are in broad agreement with the experimental results.

Nonlinear Dynamic Analysis of a Rotor-Labyrinth Seal-Bearing-Foundation System

2016 ◽  
Author(s):  
Enjie Zhang ◽  
Yinghou Jiao ◽  
Zhaobo Chen ◽  
Wenchao Mo
Keyword(s):  
Flow Velocity ◽  
Mass Flow ◽  
Nonlinear Dynamic ◽  
Labyrinth Seal ◽  
Rotor System ◽  
Inlet Pressure ◽  
Mean Flow ◽  
Dynamic Behaviors ◽  
Oil Film ◽  
Mean Flow Velocity

Steam turbine rotors are subjected to various excitation forces originated from inner structure and outer environment. Unbalance forces, nonlinear oil film forces, nonlinear seal forces, and base excitation are drastically influence the dynamic behaviors of the rotor system. A mathematical model of rotor system, including the coupled effects of these excitation forces, is established by applying the Lagrange’s equations. The axial flow velocity and leakage mass flow, which vary with the structure of labyrinth seal and with inlet/outlet pressure ratio, are calculated using the two-control-volume model. The axial mean flow velocity is then introduced into the Muszynska’s nonlinear seal forces model. The nonlinear oil-film forces are also obtained based on the short bearing theory. The equations of motion are solved by Runge-Kutta numerical integration. The influences of inlet pressure and seal strip number on axial mean flow velocity and leakage mass flow are analyzed. The effects of rotational speed, foundation movements and inlet pressure on the nonlinear dynamic characteristics of the labyrinth seal-bearing-rotor system are investigated. The bifurcation diagrams, axis orbits and spectrum cascades are used to analyze the nonlinear dynamic behaviors of the system.

scholarly journals Couple-Stress Fluid Improves Dynamic Response of Gear-Pair System Supported by Journal Bearings

2012 ◽  
Vol 2012 ◽  
pp. 1-20
Author(s):  
Cai-Wan Chang-Jian ◽  
Shiuh Ming Chang ◽  
Hsieh-Chung Hsu
Keyword(s):  
Rotational Speed ◽  
Couple Stress ◽  
Dynamic Responses ◽  
Couple Stress Fluid ◽  
Speed Ratio ◽  
Systematic Analysis ◽  
Diverse Range ◽  
Gear Mesh ◽  
Highly Nonlinear ◽  
Bearing System

A systematic analysis of the dynamic behavior of a gear-bearing system with nonlinear suspension, couple-stress fluid flow effect, nonlinear oil-film force, and nonlinear gear mesh force is performed in the present study. The dynamic orbits of the system are observed using bifurcation diagrams plotted using the dimensionless rotational speed ratio as a control parameter. The onset of chaotic motion is identified from the phase diagrams, power spectra, Poincaré maps, Lyapunov exponents and fractal dimension of the gear-bearing system. The numerical results reveal that the system exhibits a diverse range of periodic, subharmonic, quasiperiodic, and chaotic behaviors. The couple-stress fluid would be a useful lubricating fluid to suppress nonlinear dynamic responses and improve the steady of the systems. The results presented in this study provide some useful insights into the design and development of a gear-bearing system for rotating machinery that operates in highly rotational speed and highly nonlinear regimes.

An Improved Nonlinear Dynamic Model of Gear Transmission

2007 ◽  
Author(s):  
Jinyuan Tang ◽  
Siyu Chen ◽  
Changjiang Zhou
Keyword(s):  
Frequency Response ◽  
Dynamic Model ◽  
Friction Force ◽  
Nonlinear Dynamic ◽  
Nonlinear Models ◽  
Harmonic Balance Method ◽  
Gear Transmission ◽  
Force Model ◽  
Nonlinear Dynamic Model ◽  
Gear Mesh

This paper develops a new nonlinear dynamic model of gear transmission on the basis of combining friction, gear mesh stiffness and backlash. In calculating friction force, the dynamic distribution of the load along the actual line of action is taken into consideration. A new period-enlargement method is proposed to set up a friction force model and a gear meshing stiffness model. The non-linear dynamic model is a non-autonomous system. Compared with the former models, the damping coefficient and stiff coefficient in this model developed by the period enlargement method is a periodic function with the same period. Thus it is easier to apply EM (energy method) or other methods for finding the approximate analytical solution of the gear transmission dynamic equations combining with time-varying damping and stiffness. Frequency response function of the nonlinear dynamic model is obtained by using harmonic balance method. Compared the analytic and numerical results of the improved nonlinear model with that of the nonlinear models in the published papers, it is shown that: (a) the former numerical simulation techniques may not work or may result in misleading answers; (b) the coexistence of several different periodic solutions and various impacts are the same with the results in formerly published papers when gear parameters are the same. Finally, the accurate solutions of all three regimes are combined to obtain the overall frequency response of the gear pair.

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