Gear Meshing Force Research Articles

A Generalized Dynamic Model of Geared System: Establishment and Application

In order to make the dynamic characteristic simulation of the ordinary and planetary gears drive more accurate and more efficient, a generalized dynamic model of geared system is established including internal and external mesh gears in this paper. It is used to build a mathematical model, which achieves the auto judgment of the gear mesh state. We do not need to concern about active or passive gears any more, and the complicated power flow analysis can be avoided. With the numerical integration computation, the axis orbits diagram and dynamic gear mesh force characteristic are acquired and the results show that the dynamic response of translational displacement is greater when contacting line direction change is considered, and with the quickly change of direction of contacting line, the amplitude of mesh force would be increased, which easily causes the damage to the gear tooth. Moreover, compared with ordinary gear, dynamic responses of planetary gear would be affected greater by the gear backlash. Simulation results show the effectiveness of the generalized dynamic model and the mathematical model.

Extraction of angle deterministic signals in the presence of stationary speed fluctuations with cyclostationary blind source separation

This paper addresses the use of a cyclostationary blind source separation algorithm (namely RRCR) to extract angle deterministic signals from mechanical rotating machines in presence of stationary speed fluctuations. This means that only phase fluctuations while machine is running in steady-state conditions are considered while run-up or run-down speed variations are not taken into account. The machine is also supposed to run in idle conditions so non-stationary phenomena due to the load are not considered. It is theoretically assessed that in such operating conditions the deterministic (periodic) signal in the angle domain becomes cyclostationary at first and second orders in the time domain. This fact justifies the use of the RRCR algorithm, which is able to directly extract the angle deterministic signal from the time domain without performing any kind of interpolation. This is particularly valuable when angular resampling fails because of uncontrolled speed fluctuations. The capability of the proposed approach is verified by means of simulated and actual vibration signals captured on a pneumatic screwdriver handle. In this particular case not only the extraction of the angle deterministic part can be performed but also the separation of the main sources of excitation (i.e. motor shaft imbalance, epyciloidal gear meshing and air pressure forces) affecting the user hand during operations.

Chaotic responses on gear pair system equipped with journal bearings under turbulent flow

This study performs a systematic analysis of the dynamic behavior of a gear-bearing system with the turbulent flow effect, nonlinear suspension, nonlinear oil-film force and nonlinear gear mesh force. The dynamic orbits of the system are observed using bifurcation diagrams plotted using the dimensionless damping coefficient, unbalance coefficient and the dimensionless rotational speed ratio as control parameters. The onset of chaotic motion is identified from the phase diagrams, power spectra, Poincaré maps, Lyapunov exponents and fractal dimension of the gear system. The numerical results reveal that the system exhibits a diverse range of periodic, sub-harmonic and chaotic behaviors. The results presented in this study provide a detailed understanding of the operating conditions under which undesirable dynamic motion takes place in gear-bearing system and therefore offer a useful source of reference for engineers in designing and controlling such systems.

Virtual Prototype Modeling and Dynamics Analysis of a Large-Scale Wind Turbine’s Gearbox

With the gearbox of a large-scale wind turbine as a study object, the virtual prototype model of gearbox is created based on UG and ADAMS softwares according to its design parameters such as structure and size. By rigid and flexible dynamics analysis for gearbox, the angular velocity and acceleration curves of the in-out shaft are obtained. Gear meshing forces and flexible body stress cloud using ADAMS are also obtained. It is verified that these results are coincided with the theoretical value through analysis and the simulation results of ADAMS are valid. The simulation results show that the design level of wind turbine gearboxes can be improved using the virtual prototype technology and lay a good foundation for further optimal design.

A Generalized Dynamic Model of Geared System: Establishment and Application

In order to make the dynamic characteristic simulation of the ordinary and planetary gears drive more accurate and more efficient, a generalized dynamic model of geared system is established including internal and external mesh gears in this paper. It is used to build a mathematical model, which achieves the auto judgment of the gear mesh state. We do not need to concern about active or passive gears any more, and the complicated power flow analysis can be avoided. With the numerical integration computation, the axis orbits diagram and dynamic gear mesh force characteristic are acquired and the results show that the dynamic response of translational displacement is greater when contacting line direction change is considered, and with the quickly change of direction of contacting line, the amplitude of mesh force would be increased, which easily causes the damage to the gear tooth. Moreover, compared with ordinary gear, dynamic responses of planetary gear would be affected greater by the gear backlash. Sim...

The bifurcation and chaos of a gear pair system based on a strongly non-linear rotor—bearing system

A systematic analysis of the dynamic behaviours of a gear pair system based on a rotor—bearing system under strongly non-linear effects (i.e. non-linear suspension effect, non-linear oil-film force, non-linear rub-impact force, and non-linear gear mesh force) is presented in this study. The dynamic orbits of the system are observed using bifurcation diagrams plotted using the dimensionless unbalance coefficient, the dimensionless damping coefficient, and the dimensionless rotational speed ratio as control parameters. The onset of chaotic motion is specified from the phase diagrams, power spectra, Poincaré maps, Lyapunov exponents, and fractal dimension of the system. There exists various forms of periodic, quasi-periodic, and chaotic motions at different bifurcation parameters. The simulation results also found that highly non-periodic motions do exist in gear—rotor—bearing systems under those non-linear effects. The results presented in this study provide a better understanding of the operating conditions under which undesirable dynamic motion takes place in a gear—bearing system; they would therefore serve as a useful source of reference for engineers in designing and controlling such systems.

Non-linear dynamic analysis of a HSFD mounted gear-bearing system

An investigation is carried out on the systematic analysis of the dynamic behavior of the hybrid squeeze-film damper (HSFD) mounted a gear-bearing system with strongly non-linear oil-film force and gear meshing force in the present study. The dynamic orbits of the system are observed using bifurcation diagrams plotted using the dimensionless unbalance coefficient, damping coefficient and the dimensionless rotating speed ratio as control parameters. The non-dimensional equations of the gear-bearing system are solved using the fourth order Runge-Kutta method. The onset of chaotic motion is identified from the phase diagrams, power spectra, Poincare maps, bifurcation diagrams, maximum Lyapunov exponents and fractal dimension of the gear-bearing system. 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 rotating speed and highly non-linear regimes.

유성기어세트의 소음 진동 거동에 대한 해석 및 실험적 연구

In this paper, Verification of the qualitatively identical relationships existing between simulation data and experimental results allowed for a new analysis procedure of a planetary gear set -- in an automatic transmission -- to be conducted. Tooth profiles were found to be crucial to the gear mesh forces of the planetary gear set. Based on Kahraman's Model, dynamic resonances of the planetary gear set were found to be out of operating range. Most importantly, a 2DPLANETARY FEM program, an innovative design tool for planetary gear sets, was utilized.

Nonlinear analysis for gear pair system supported by long journal bearings under nonlinear suspension

A systematic analysis of the dynamics of a gear pair system supported by journal bearings is performed in this study. Nonlinear suspension effect, nonlinear oil-film force and nonlinear gear mesh force are all also considered in this study. The dynamic orbits of the system are observed using bifurcation diagrams plotted using the dimensionless damping ratios and the dimensionless rotational speed ratio as control parameters. The onset of chaotic motion is identified from the phase diagrams, power spectra, Poincaré maps, and Lyapunov exponents of the gear-bearing system. The numerical results reveal that the system exhibits a diverse range of periodic, sub-harmonic and chaotic behaviors. The results presented in this study provide an understanding of the operating conditions under which undesirable dynamic motion takes place in a gear-bearing system and therefore serve as a useful source of reference for engineers in designing and controlling such systems.

A dynamic model to predict modulation sidebands of a planetary gear set having manufacturing errors

In this study, a nonlinear time-varying dynamic model is proposed to predict modulation sidebands of planetary gear sets. This discrete dynamic model includes periodically time-varying gear mesh stiffnesses and the nonlinearities associated with tooth separations. The model uses forms of gear mesh interface excitations that are amplitude and frequency modulated due to a class of gear manufacturing errors to predict dynamic forces at all sun-planet and ring-planet gear meshes. The predicted gear mesh force spectra are shown to exhibit well-defined modulation sidebands at frequencies associated with the rotational speeds of gears relative to the planet carrier. This model is further combined with a previously developed model that accounts for amplitude modulations due to rotation of the carrier to predict acceleration spectra at a fixed position in the planetary transmission housing. Individual contributions of each gear error in the form of amplitude and frequency modulations are illustrated through an example analysis. Comparisons are made to measured spectra to demonstrate the capability of the model in predicting the sidebands of a planetary gear set with gear manufacturing errors and a rotating carrier.

Strong nonlinearity analysis for gear-bearing system under nonlinear suspension—bifurcation and chaos

This study performs a systematic analysis of the dynamic behavior of a gear-bearing system with nonlinear suspension, nonlinear oil-film force, and nonlinear gear mesh force. The dynamic orbits of the system are observed using bifurcation diagrams plotted with both the dimensionless unbalance coefficient and the dimensionless rotational speed ratio as control parameters. The onset of chaotic motion is identified from the phase diagrams, power spectra, Poincaré maps, Lyapunov exponents, and fractal dimensions of the gear-bearing system. The numerical results reveal that the system exhibits a diverse range of periodic, sub-harmonic, and chaotic behaviors. The results presented in this study provide an understanding of the operating conditions under which undesirable dynamic motion takes place in a gear-bearing system and therefore serves as a useful source of reference for engineers in designing and controlling such systems.

Construction of an Estimating System of Gear Noise using Thermography

We proposed a new estimating method of a high-speed and high accurate tooth contact by using thermography. This method has aimed to short the measurement time, and to know an accurate tooth contact area and the strength of the surface pressure by measuring the heat generated at the time of meshing gear teeth without contact. First, the radiation performance on the gear tooth surface was investigated as a basic experiment, and the effect of lubricantion was examined. Moreover, experimental conditions were researched. Next, the reliability of the present method for measuring the surface temperature distribution was evaluated by comparing with the result obtained by paints. The surface pressure on the tooth surface was estimated based on obtained temparature distribution on the gear tooth surface. Finally, we made an attempt to predict the gear meshing force based on the proposed estimating method.

DYNAMIC ANALYSIS OF A SPUR GEAR BY THE DYNAMIC STIFFNESS METHOD

This study treats a spur gear tooth as a variable cross-section Timoshenko beam to construct a dynamic model, being able to obtain transient response for spur gears of involute profiles. The dynamic responses of a single tooth and a gear pair are investigated. Firstly, polynomials are used to represent the gear blank and the tooth profile. The dynamic stiffness matrix and natural frequencies of the gear are in turn calculated. The forced response of a tooth subject to a shaft-driven transmission torque is calculated by performing modal analysis. This study takes into account time-varying stiffness and mass matrices and the gear meshing forces at moving meshing points. The forced response at arbitrary points in a gear tooth can be obtained. Calculation results of fillet stresses and strains are compared with those in the literature to verify the proposed method.

DETERMINATION OF COMPONENT MOTIONS IN A MOTOR-OPERATED VALVE USING HOUSING VIBRATION

This paper is concerned with diagnosing the construction of motor operated valves (MOVs) based on their performance in previous runs. One part of the signature that reveals condition is valve travel, which is to be determined non-invasively. The technique described here is based on the determination of valve stem rotation through the analysis of gear meshing forces. These forces are, in turn, determined from the vibrations they produce in the MOV housing. These vibrations are interpreted as forces through inverse filtering of the received signals. The gear mesh force signals are, in turn, related to gear rotation through frequency demodulation. Experimental results from a laboratory set-up indicate that this procedure leads to acceptable estimates of shaft rotation and valve travel.

Modal simulation of gear box vibration with experimental correlation

A newly developed global dynamic model was used to simulate the dynamics of a gear noise rig at NASA Lewis Research Center. Experimental results from the test rig were used to verify the analytical model. In this global dynamic model, the number of degrees of freedom of the system are reduced by transforming the system equations of motion into modal coordinates. The vibration of the individual gear-shaft system are coupled through the gear mesh forces. A three-dimensional, axial-lateral coupled, bearing model was used to couple the casing structural vibration to the gear-rotor dynamics. The coupled system of modal equations is solved to predict the resulting vibration at several locations on the test rig. Experimental vibration data was compared to the predicitions of the global dynamic model. There is excellent agreement between the vibration results from analysis and experiment.