Floating Sun Gear Research Articles

Experimental and Theoretical Investigation of Quasi-Static System Level Behavior of Planetary Gear Sets

Abstract This study presents a unique experimental methodology that synchronously measures various quasi-static responses of a simple four-planet planetary gear set, namely, planet load sharing, overall transmission error (OTE), and floating sun gear orbits. Strain gauges mounted directly on the planet pins were used to monitor the load shared among the planets, which is a crucial design criterion for durability and performance. High-precision optical encoders were used to measure the OTE of the gear set to explore its diagnostic value in identifying system errors. Radial motions of the floating sun gear, which are critical to the self-centering and load sharing behavior of the gear set, were monitored using magnetic proximity probes. The influence of various design parameters and operating conditions such as planet mesh phasing, carrier pin position errors, gear tooth modifications, and input torque on the system’s response will be investigated by performing an extensive set of experiments in a repeatable and accurate manner. Finally, these experimental results will be recreated theoretically using the static planetary load distribution model of Hu et al. (2018, “A Load Distribution Model for Planetary Gear Sets,” ASME J. Mech. Des., 140(5), p. 53302) to not only validate the model but also comprehend the measured behavior.

Analytical investigation on load sharing characteristics of herringbone planetary gear train with flexible support and floating sun gear

As an important part of reducers, herringbone planetary gear train (HPGT) has the advantages of small size, small mass, large transmission ratio, compact structure and strong carrying capacity. It has wide applications in the transmission fields such as aviation and ships. The flexible support stiffness and the floating components are largely influencing the load sharing characteristic, which is a key indicator to evaluate the bearing stability and reliability of planet gears. Therefore, it is necessary to study the influence mechanism of flexible support on the load sharing characteristic with floating sun gear. Based on the centralized parameters theory and the Lagrange method, a dynamic model for HPGT is established. At the same time, based on this model, natural characteristic is also researched. Particularly, the dynamic curves are expressed in a form of polar coordinate system, which can make the curves clearly show the changing law of dynamic characteristics. As shown in the studied results, when the sun gear is normally supported and the sun gear is floating, the natural frequency of the HPGT is calculated, and the influence mechanism of the flexible support on the load sharing characteristics is studied. In addition, the difference in load sharing characteristic is compared.

Vibration modulation sidebands mechanisms of equally-spaced planetary gear train with a floating sun gear

Abstract The sun gear of planetary gear train is generally designed to float in the radial direction to achieve the uniform load distribution among different planet gears, but brings periodic gear mesh errors to generate more complicated vibration signals. There lack effective feature indicators for fault diagnosis at present. On the basis of researches on signal transfer path functions and measuring-direction projection functions of the gear mesh force, a set of vibration signal models are built to represent the modulation sidebands induced by a single planet gear mesh. Taking phase differences among equally-spaced planet gears into consideration, vibration modulation sidebands generating from meshes of multiple planet gears are further studied. The mechanisms of sidebands are obtained, especially the influences of floating sun gear on some specific frequency components. Vibration signals of a single-stage planetary gear train and a wind turbine planetary gearbox show good frequency consistencies with the model-based signal. The comparison analyses effectively verify the correctness of the proposed model. An important feature indicator is obtained to distinguish whether the planetary gear train is assembled with a floating sun gear, or whether the planetary gear train without a floating sun gear exists some distributed defects.

Dynamics modeling and vibration modulation signal analysis of wind turbine planetary gearbox with a floating sun gear

In wind turbine planetary gearboxes, the sun gears are generally designed to float in the radial direction to achieve the uniform load distribution among different planet gears, but will lead to gear mesh errors and cause complicated vibration signals on the contrary. The floating sun gear is misdiagnosed as a distributed defect easily. Additionally, the floating sun gear's rotating motion and excitation force are too disorderly to be characterized by mathematical or empirical formulas. In the paper, a set of rigid-flexible coupling dynamics models of planetary gear train are built to research vibration characteristics of the floating sun gear under different conditions. Depend on the model-based vibration analysis, the rotating motion of floating sun gear is revealed well, which can be characterized by its frequency features, meanwhile mechanisms of modulation sidebands indicating different kinds of defects are deduced clearly. The experimental data keep good consistency with the simulation signals, which verifies the validity of the proposed well. Vibration feature indicators are obtained to distinguish fault signals and diagnose the distributed or localized defect of floating sun gear effectively, which is helpful to avoid the misdiagnosis of floating sun gear.

Influence of the Eccentric Error of Star Gear on the Bifurcation Properties of Herringbone Star Gear Transmission with Floating Sun Gear

Taking a herringbone star gear transmission (HSGT) with floating sun gear as an example, the system bifurcation characteristics with the changing of the eccentric error of star gear and the working frequencies are analyzed. For this analysis, a generalized dynamic model of HSGT considering the manufacturing eccentric errors, time‐varying mesh stiffness, and load balancing mechanism is established and solved by numerical method. The floating process of sun gear is explained. In this paper, there are seven cases about the eccentric errors of star gears which are calculated, respectively. To study the effect of the working frequencies (including meshing frequency and rotation frequency), the calculation is done at three kinds of input speed in which the working frequencies are close to the system natural frequencies. The results are demonstrated in detail by the bifurcation diagrams, phase plane plots, and Poincare maps. The system bifurcation characteristics are particularly analyzed and compared in every case. This work provides important guidance to the engineering of HSGT.

M-DOF dynamic model for load sharing behavior analysis of PGT

A Multi-degree-of-freedom (M-DOF) nonlinear dynamic model for n-pinion Planetary gear train (PGT) is presented in this paper to investigate load sharing behavior of planet gears. In this dynamic model, manufacturing and assembly errors, elastic deformation and time-varying mesh stiffness are considered. Two sets of elastic compatibility equations are proposed to describe compatibility relationship between displacements, errors and elastic deformations. By means of Ishikawa formula, time-varying mesh stiffness of the gear pair is determined. The dynamic motion equations are solved with Runge-Kutta numerical integral method, which yields the displacements and deformations of each component. With the model, dynamic load sharing behavior of planet gears is evaluated. An example of 3-pinion PGT dynamic modeling is included, for which the influence of floating sun gear and adding flexible planet pin on the load sharing characteristics is analyzed.

Effects of floating sun gear in a wind turbine's planetary gearbox with geometrical imperfections

This paper addresses the effect of gear geometrical errors in wind turbine planetary gearboxes with a floating sun gear. Numerical simulations and experiments are employed throughout the study. A National Renewable Energy Laboratory 750 kW gearbox is modelled in a multibody environment and verified using the experimental data obtained from a dynamometer test. The gear geometrical errors, which are both assembly dependent and assembly independent, are described, and planet-pin misalignment and eccentricity are selected as the two most influential and key errors for case studies. Various load cases involving errors in the floating and non-floating sun gear designs are simulated, and the planet-bearing reactions, gear vibrations, gear mesh loads and bearing fatigue lives are compared. All tests and simulations are performed at the rated wind speed. For errorless gears, the non-floating sun gear design performs better in terms of gear load variation, whereas the upwind planet bearing has more damage. In the floating sun gear scenario, the planet misalignment is neutralized by changing the sun motion pattern and the planet gear's elastic deformation. The effects of gear profile modifications are also evaluated, revealing that profile modifications such as crowning improve the effects of misalignment. Copyright © 2014 John Wiley & Sons, Ltd.

Gear meshing analysis of planetary gear sets with a floating sun gear

The goal of this study is to propose an analytical approach for analysis of gear meshing in a planetary gear set with a floating sun gear. With focus on the basic geometrical relation, we derive a set of equations based on the exact involute gear geometry for calculation of the tooth clearances among engaged unmodified or modified flanks of gears having relevant errors. Two constraint conditions for the floating sun gear are established for determination of the movable area. Numerical examples are presented to explore the influences of the planet gear number, the backlashes, and the assembly/manufacturing errors on the tooth clearance, the moveable area and assemblability of the sun gear.

410 部品誤差がスター型遊星歯車装置ねじり共振に与える影響

The influence of the positioning error, the eccentricity or shape error, which is made during the milling process, at the planetary gear center or the internal gear of the star type planetary gear trains to the torsional resonance are discussed using the simulating program. The program was previously confirmed that it can sufficiently simulate the vibration occurrence speed of the rotational shaft and the vibration orbit of the floating sun gear. In the conclusion, the position error of the internal gear center and the planetary gear center make the change of the self-centering position of the floating sun gear and the shape of the movable area of the sun gear. But they are not the cause of the resonance, because the resonance does not occur without the forced torque. The eccentricity of the planetary gear can be the cause of the resonance when the rotation speed of the planetary gear becomes the natural frequency of the rotating shaft. But the eccentricity of the internal gear is not the cause of the resonance. The triangle shape error of the internal gear, which is measured in the experiment, also simulated. And it is made clear that the shape error can be the cause of the resonance. This can be considered that the transmission error can be made by the coincidence of the shape and the number of planetary gears.

Self-centering Path and Abnormal Vibration Orbit of Floating Sun Gear in Star-Type Planetary Gear Train. Numerical Simulation Considering Effects of Friction Force Acting on Contact Teeth.

Both self-centering path and abnormal vibration orbit of a floating sun gear shaft in a star-type planetary gear train are numerically simulated taking account of effects of friction forces acting on gear teeth instead of viscous damping forces. The simulation model is composed of a floating sun gear with three degrees of freedom x, y and θ and six meshing springs with backlash. Equations of motion of the sun gear are solved by the Runge-Kutta method. Firstly, the static friction coefficient was determined by experiments. In the simulation, it is used for obtaining the self-centering path, while the dynamic friction coefficient is assuumed for obtaining the abnormal vibration orbit. The self-centering path depends on the initial position of the sun gear in the experiment. The self-centering simulation considering the friction force gives the same results as the experimental ones. It is also shown that the simulation of abnormal vibration orbit gives the good accordance with the experimental results when the friction forces instead of the damping forces are accounted in the model.

Simulation on Abnormal Vibration of Floating Sun Gear in Star-Type Planetary Gear Train.

Floating gear mechanism is widely used in planetary gear trains to share a transmitted load equally with planet gears. Our experiments show that this mechanism causes an abnormal lateral vibration of the floating gear when a large torsional resonance occurs. This paper proposes a dynamic model and simulation method for analyzing the abnormal lateral vibration of floating sun gear shaft in a star-type planetary gear train. The dynamic model is composed of a motor, planetary gear train and dynamometer, which is the same as our experimental apparatus. The total degree of freedom of the model is 15. The gears are connected each other by 12 springs with backlash modeling the mesh between gear teeth. An pulsating torque of the motor is considered. The simulated results are in good accordance with the experimental ones as for vibration wave forms and resonance curves and also show how to prevent the abnormal vibration.

Self-Centering Path and Abnormal Vibration Orbit of Floating Sun Gear in Star-Type Planetary Gear Train.

Both self centering path and abnormal vibration orbit of a floating sun gear shaft in a star type planetary gear train which were observed in the experiments are numerically simulated with a simple dynamic model. The model is composed of a floating sun gear with three degree of freedom x, y and θ and meshing springs with backlash which support the sun gear. Effects of the gravitational force and applied exciting torque are also considered in the model. Equations of motion are solved by the Runge Kutta method under the conditions that a frequency of applied exciting torque is very small to obtain the selfcentering path, or it is equal to a torsional natural frequency of the model to obtain the abnormal vibration orbit. The simulated results are in good accordance with the experimental ones.

Self-Centering Characteristics of Floating Sun Gear in a Star-Type Planetary Gear Train.

A floating gear mechanism is often adopted in planetary gear design in order to share the load torque equally among planetary gears. The floating gear has no bearings and produces a self-centering nature. When the load torque is not applied, the floating gear lies at the bottom of the backlash area due to gravity, and it travels to the center position of the planetary gear train along several paths when the torque is applied. This path is called a self-centering locus. This paper experimentally and theoretically clarifies the self-centering locus, the relationship between the applied torque and the locus, and the minimum torque required to complete the self-centering process.

Torsional Vibrations and Dynamic Loads in a Basic Planetary Gear System

An interative method has been developed for analyzing dynamic loads in a light weight basic planetary gear system. The effects of fixed, semi-floating, and fully-floating sun gear conditions have been emphasized. The load dependent variable gear mesh stiffnesses were incorporated into a practical torsional dynamic model of a planetary gear system. The dynamic model consists of input and output units, shafts, and a planetary train. In this model, the sun gear has three degrees of freedom; two transverse and one rotational. The planets, ring gear, and the input and output units have one degree of freedom, (rotation) thus giving a total of nine degrees of freedoms for the basic system. The ring gear has a continuous radial support. The results indicate that the fixed sun gear arrangement with accurate or errorless gearing offers in general better performance than the floating sun gear system.