A numerical method for calculating the misalignments of planetary gears

Author(s):  
Chi Zhou ◽  
Qi Wang ◽  
Liangjin Gui ◽  
Zijie Fan

Because misalignments derived from the deflections of transmission systems have significant effects on the load capacity of planetary gears, these misalignments should be accurately considered in the analysis of planetary gears. Here, we develop a new approach for misalignment calculations of cylindrical planetary gears. A nonlinear model of a planetary gear transmission system is built based on the finite element method and nonlinear bearing theory for misalignment calculations that can precisely simulate the structural characteristics and mechanical properties of a planetary gear system. The nonlinear static equation of a planetary system is solved efficiently using the Newton–Raphson method. Gear misalignments of all the planet branches are determined by the results of the system static analysis. The reliability and advantages of the proposed method are discussed via case studies. The effects of including the variation of the planet positions and the nonlinearity of the bearing stiffness on the planetary gear misalignments under different load conditions are studied. The misalignments can be reliably determined using the proposed method for calculating the load capacity of planetary gears.

Author(s):  
Jonas Gnauert ◽  
Felix Schlüter ◽  
Georg Jacobs ◽  
Dennis Bosse ◽  
Stefan Witter

AbstractWind turbines (WT) must be further optimized concerning availability and reliability. One of the major reasons of WT downtime is the failure of gearbox bearings. Some of these failures occur, due to the ring creep phenomenon, which is mostly detected in the planetary bearings. The ring creep phenomenon describes a relative movement of the outer ring to the planetary gear. In order to improve the understanding of ring creep, the finite element method (FEM) is used to simulate ring creep in planetary gears. First, a sensitivity analysis is carried out on a small bearing size (NU205), to characterize relevant influence parameters for ring creep—considered parameters are teeth module, coefficient of friction, interference fit and normal tooth forces. Secondly, a full-scale planetary bearing (SL185030) of a 1MW WT is simulated and verified with experimental data.


2021 ◽  
Vol 104 (3) ◽  
pp. 003685042110356
Author(s):  
Hexu Yang ◽  
Xiaopeng Li ◽  
Jinchi Xu ◽  
Zemin Yang ◽  
Renzhen Chen

According to the working characteristics of a 1.5 MW wind turbine planetary gear system under complex and random wind load, a two-parameter Weibull distribution model is used to describe the distribution of random wind speed, and the time-varying load caused by random wind speed is obtained. The nonlinear dynamic model of planetary gear transmission system is established by using the lumped parameter method, and the relative relations among various components are derived by using Lagrange method. Then, the relative relationship between the components is solved by Runge Kutta method. Considering the influence of random load and stiffness ratio on the planetary gear transmission system, the nonlinear dynamic response of cyclic load and random wind load on the transmission system is analyzed. The analysis results show that the variation of the stiffness ratio makes the planetary gear have abundant nonlinear dynamics behavior and the planetary gear can get rid of chaos and enter into stable periodic motion by changing the stiffness ratio properly on the premise of ensuring transmission efficiency. For the variable pitch wind turbine, the random change of external load increases the instability of the system.


2013 ◽  
Vol 569-570 ◽  
pp. 489-496 ◽  
Author(s):  
Yong Gui ◽  
Qin Kai Han ◽  
Zheng Li ◽  
Zhi Ke Peng ◽  
Fu Lei Chu

Tooth breakage is a typical failure form of wind-turbine planetary gear transmission system, it is important to study the influence of tooth breakage on vibration characteristics of planetary gear transmission system. In this paper, considering the tooth breakage defect, a lumped parameter vibration model of a planetary gear system with time-periodic mesh stiffness is established. Effects of the length and width of tooth breakage on meshing stiffness and dynamic response are discussed in detail. The relation between characteristic frequency of the tooth breakage fault and rotating speeds is pointed out. Several statistical indicators are utilized to show the influence of two parameters (length of planet tooth breakage and input speed) on the dynamic response of the system. Experiments are carried out to verify the simulation results. These results would be useful for fault diagnosis of wind turbine transmission system at different operation conditions.


Author(s):  
Kuo Jao Huang ◽  
Shou Ren Zhang

A finite element (FE) method is used to analyze modal and dynamic behavior of planetary gear systems (PGSs) focusing on the effect of bearing and carrier stiffness. Using derived tooth profile equations, elements for gear can be parametrically created. Then, the 2D/3D FE models of a planetary gear system (PGS) are constructed. Accordingly, structural natural frequencies and modal shapes are calculated after adequately assigning the material, boundary conditions, and tooth contact of gear pairs. An index, namely dimensionless slope, is defined to reflect the modal property due to the bearing stiffness change. Influence of carrier material and gear bearing stiffnesses on modal behavior is investigated. Several results of the PGS modal characteristics affected by the material and bearing stiffness are also obtained. Besides, the dynamic responses of the PGSs are analyzed under the carrier rotation. Finally, dynamic fillet stress and loading inequality among gear pairs due to planet bearing stiffness variation are analyzed. The FE approach presented can conveniently demonstrate modal and dynamic behaviors of PGSs.


Author(s):  
Jingyue Wang ◽  
Ning Liu ◽  
Haotian Wang ◽  
Lixin Guo

Abstract In order to study the influence of friction on the nonlinear dynamic characteristics of a planetary gear system, the dynamic model of a planet gear transmission system considering mixed elastohydrodynamic lubrication (EHL) friction, time-varying meshing stiffness, backlash and comprehensive meshing error is established. The Runge–Kutta method is used to solve the dynamic differential equations, and the bifurcation and chaos characteristics of the system are analysed through the bifurcation diagram, largest lyapunov exponent (LLE), Poincaré map, phase diagram, time history curve diagram and fast fourier transform (FFT)spectrum. The results of numerical simulation show that the planetary gear system with mixed EHL friction exhibits rich bifurcation characteristics, and the system experiences short-periodic motion, long-periodic motion, quasi-periodic motion and chaotic motion. The effect of tooth surface friction on the bifurcation characteristics of the planetary gear system is more obvious at high frequency than that at low frequency. Tooth surface friction causes the system to enter chaotic motion in advance.


Author(s):  
F.I. Plekhanov ◽  
E.F. Vychuzhanina

Planetary gears are commonly used in drive technology due to their high load capacity and good weight and size parameters. Among planetary gears, multi-satellite structures with a minimum number of excessive links are most widely used. They have a close to uniform distribution of the load in the engaged gears, which has a positive effect on the strength and bearing capacity of the drive. Such designs include planetary gears, the satellites of which are mounted on spherical bearings, and one of the main links (most often the sun gear) is self-aligning. This provides a theoretically uniform distribution of the load in the engaged gears when the mechanism has three satellites. However, high-loaded drives often use designs with a large number of satellites where the load is distributed unevenly due to gear manufacturing errors. The deformability of individual transmission elements has a significant positive effect on the distribution of the load in the gears, thus compensating for the manufacturing errors. In view of this, the authors propose a multi-satellite planetary gear with a carrier made with grooves in the cheeks, which reduces their rigidity and provides, with a rational choice of the parameters of the mechanism, an increase in the mechanism’s bearing capacity. When determining the carrier cheek’s compliance, two schemes of loading in the coupling zone with the axis of the satellite (uniform and nonuniform) are considered. The solution is obtained using Mohr’s integrals. A numerical analysis of the stressed-strain state of the carrier cheek performed using the finite element method in the SolidWorks environment showed that the results of the analysis were close to the theoretical ones. They corresponded to a uniform load distribution in the coupling zone of the satellite axis and the carrier cheek. The obtained dependences can be used in the design of a mechanical drive to determine the coefficients of the uneven load distribution over the planetary gear satellites and over the individual crowns of the satellite.


2013 ◽  
Vol 135 (3) ◽  
Author(s):  
Zaigang Chen ◽  
Yimin Shao

Planetary gears are widely used in the industry due to their advantages of compactness, high power-to-weight ratios, high efficiency, and so on. However, planetary gears such as that in wind turbine transmissions always operate under dynamic conditions with internal and external load fluctuations, which accelerate the occurrence of gear failures, such as tooth crack, pitting, spalling, wear, scoring, scuffing, etc. As one of these failure modes, gear tooth crack at the tooth root due to tooth bending fatigue or excessive load is investigated; how it influences the dynamic features of planetary gear system is studied. The applied tooth root crack model can simulate the propagation process of the crack along tooth width and crack depth. With this approach, the mesh stiffness of gear pairs in mesh is obtained and incorporated into a planetary gear dynamic model to investigate the effects of the tooth root crack on the planetary gear dynamic responses. Tooth root cracks on the sun gear and on the planet gear are considered, respectively, with different crack sizes and inclination angles. Finally, analysis regarding the influence of tooth root crack on the dynamic responses of the planetary gear system is performed in time and frequency domains, respectively. Moreover, the differences in the dynamic features of the planetary gear between the cases that tooth root crack on the sun gear and on the planet gear are found.


2014 ◽  
Vol 15 (11) ◽  
pp. 2357-2366 ◽  
Author(s):  
Wei Sun ◽  
Xin Ding ◽  
Jing Wei ◽  
Xinglong Hu ◽  
Qingguo Wang

Author(s):  
Tae Ho Kim ◽  
Moon Sung Park ◽  
Jongsung Lee ◽  
Young Min Kim ◽  
Kyoung-Ku Ha ◽  
...  

Gas foil bearings (GFBs) have clear advantages over oil-lubricated and rolling element bearings, by virtue of low power loss, oil-free operation in compact units, and rotordynamic stability at high speeds. However, because of the inherent low gas viscosity, GFBs have lower load capacity than the other bearings. In particular, accurate measurement of load capacity and dynamic characteristics of gas foil thrust bearings (GFTBs) is utmost important to widening their applications to high performance turbomachinery. In this study, a series of excitation tests were performed on a small oil-free turbomachinery with base excitations in the rotor axial direction to measure the dynamic load characteristics of a pair of six-pad, bump-type GFTBs, which support the thrust collar. An electromagnetic shaker provided dynamic sine sweep loads to the test bench (shaking table), which held rigidly the turbomachinery test rig for increasing excitation frequency from 10 Hz to 200 Hz. The magnitude of the shaker dynamic load, represented as an acceleration measured on the test rig, was increased up to 9 G (gravity). An eddy current sensor installed on the test rig housing measured the axial displacement (or vibrational amplitude) of the rotor thrust collar during the excitation tests. The axial acceleration of the rotor relative to the test rig was calculated using the measured displacement. A single degree-of-freedom base excitation model identified the frequency-dependent dynamic load capacity, stiffness, damping, and loss factor of the test GFTB for increasing shaker dynamic loads and increasing bearing clearances. The test results show that, for a constant shaker force and the test GFTB with a clearance of 155 μm, an increasing excitation frequency increases the dynamic load carried by the test GFTB, i.e., bearing reaction force, until a certain value of the frequency where it jumps down suddenly because of the influence from Duffing’s vibrations of the rotor. The bearing stiffness increases and the damping decreases dramatically as the excitation frequency increases. Generally, the bearing loss factor ranges from 0.5 to 1.5 independent of the frequency. As the shaker force increases, the bearing dynamic load, stiffness, damping, and loss factor increase depending on the excitation frequency. Interestingly, the agreements between the measured GFTB dynamic load versus the thrust runner displacement, the measured GFTB static load versus the structural deflection, and the predicted static load versus the thrust runner displacement are remarkable. Further tests with increasing GFTB clearances of 155, 180, 205, and 225 μm revealed that the vibrational amplitude increases and the jump-down frequency decreases with increasing clearances. The bearing load increases, but the bearing stiffness, damping, and loss factor decrease slightly as the clearance increases. The test results after a modification of the GFTB by rotating one side bearing plate by 30° relative to the other side bearing plate revealed insignificant changes in the dynamic characteristics. The present dynamic performance measurements provide a useful database of GFTBs for use in microturbomachinery.


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