Nonlinear modelling and transient dynamics analysis of a hoist equipped with a two-stage planetary gear transmission system

A system-level nonlinear dynamic model for a two-stage planetary gear transmission system of a hoist is established with the consideration of time-varying meshing stiffness, backlash, damping, and bearing stiffness. Vibrational test results are also presented in accordance with simulation results computed from the dynamic model, and engagement-impacting dynamic simulations are achieved by adapting a dynamic explicit algorithm based on this model. Accordingly, variation in the contact state in relation to the engaging position is obtained together with vibration characteristics of the transmission system. This study provides a theoretical basis for the reduction of vibration and noise for the transmission system

Vibrational analysis of planetary gear trains by finite element method

Planetary gear trains produce several advantages, including high speed reduction, compactness, greater load sharing and higher torque to weight ratio, which are used widely in wind turbine, automobiles, robot and other applications. In some important transmission applications, the noise and vibration are key concerns in design. In this paper, a 3D dynamic contact and impact analysis model of planetary gear trains has been proposed. Tooth surface friction, backlash, tolerance of peg hole, and time-varying stiffness were considered in this dynamic model. The ANSYS / LS-DYNA were utilized to analyze the dynamic responses of gear transmission of the planetary gears. The vibration behavior of an actual gear set under dynamic loading was simulated in the dynamic model. The stiffness and elastic deformation of gear teeth are calculated using the finite element method with actual geometry and positions of the gears. The time-varying position of the carrier defined as the vibration and noise source. After impact analysis, the numerical results of vibration of carrier involved with the transient and steady states. Through the Fast Fourier Transform (FFT) methods, frequency spectrums of the transient and steady states of the calculated vibration of planet carrier are obtained for the gearbox designer to avoid the resonance zone

Dynamic behavior of the nonlinear planetary gear model in nonstationary conditions

The nonlinear effects in gearboxes are a key concern to describe accurately their dynamic behavior. This task is difficult for complex gear systems such as planetary gearboxes. The main aim of this work is provide responses to overcome this difficulty especially in non-stationary operating regimes by investigating a back-to-back planetary gearbox in steady conditions and in run up regime. The nonlinear Hertzian contact of teeth pair is modeled in stationary and non-stationary run-up regime. Then it is incorporated to a torsional model of the planetary gearbox through the different mesh stiffness functions. In addition, motor torque and external load variation are taken into account. The nonlinear equations of motion of the back-to-back planetary gearbox are computed through the Newmark-β algorithm combined with the method of Newton-Raphson. An experimental validation of the proposed numerical model is done through a test bench for both stationary and run-up regimes. The vibration characteristics are extracted and correlated to speed and torque. Time frequency analysis is implemented to characterize the transient regime during run-up.This research work was supported by the Spanish Ministry responsible of Science and Technology through the project DPI2017-85390-P. The authors gratefully thank the University of Cantabria cooperation project which supports the doctoral trainings of students of Sfax University. The authors also acknowledge the Tunisian Project No. “19PEJC10-06”

CAE Methods on Vibration-based Health Monitoring of Power Transmission Systems

This thesis focuses on different methods to analyze power transmission systems with computer software to aid in detection of faulty or damaged systems. It is split into three sections. The first section involves utilizing finite element software to analyze gear stiffness and stresses. A quasi-static and dynamic analysis are done on two sets of fixed axis spur gears and a planetary gear system using ABAQUS to analyze the stress, strain and gear mesh stiffness variation. In the second section, the vibrational patterns produced by a simple bevel gear system are investigated by an experiment and by dynamic modeling in ADAMS. Using a Fast Fourier Transform (FFT) on the dynamic contact forces, a comprehensive frequency-domain analysis will reveal unique vibration spectra at distinct frequencies around the gear mesh frequencies, their super- and sub- harmonics, and their side-band modulations. ADAMS simulation results are then compared with the experimental results. Constraints, bearing resistant torques, and other key parameters are applied as closely as possible to real operating conditions. The third section looks closely at the dynamic contact forces of a practical two-stage planetary gear. Using the same FFT approach in the second section, a frequency-domain analysis will reveal distinct frequencies around both the first-stage and the second-stage gear mesh frequencies, and their harmonics. In addition, joint time-frequency analysis (JTFA) will be applied to damaged and undamaged planetary gear systems with transient start-up conditions to observe how the frequency contents of the contact force evolve over time

Effect of load and meshing stiffness variation on modal properties of planetary gear

Modal analysis of mechanical transmissions allows identification of critical frequencies and corresponding vibration modes. Major research works are done under constant loading conditions. However, load fluctuation can lead to variability in stiffness characteristics. Also, in the case of gear transmission, the fluctuation of mesh stiffness is rarely considered in the modal analysis. In this paper, a modal analysis of planetary gear transmission is investigated for different loading conditions and under mesh stiffness fluctuation. Hammer impact tests are carried out and the vibrations on fix ring are measured with different levels of load. During each test, natural frequencies are identified through frequency response function. The obtained results are correlated against the corresponding tridimensional lumped parameter of the test rig. Distributions of modal strain and kinetic energy for different loading conditions are studied as well as the effect of mesh stiffness variation on the natural frequencies.This paper was financially supported by the Tunisian-Spanish Joint Project No. A1/037038/11. The authors would like also to acknowledge project ‘‘Development of methodologies for the simulation and improvement of the dynamic behavior of planetary transmissions DPI2013-44860” funded by the Spanish Ministry of Science and Technology. Acknowledgment to the University of Cantabria cooperation project for doctoral training of University of Sfax’s students

Research on vibration characteristics of gear-coupled multi-shaft rotor-bearing systems under the excitation of unbalance

To find out the effect of eccentricity of a gear wheel on inherent characteristics of a gear-rotor system, this paper establishes a pair of general transverse-rotational-axial-swinging multi degrees of freedom coupling helical gear meshing dynamic model based on the finite element method (FEM). Considering the influence of the azimuth, the meshing angle, the helix angle and the rotation direction of driving shaft on mesh stiffness matrix, it analyzes the effect of mesh stiffness and mesh damping on the inherent characteristics and the transient response of the system. It obtains the displacement response curve and the dynamic meshing force curve of all nodes responding to the incentives of static transmission error and unbalance while considering mesh damping. It concludes that the effects of gear coupling and eccentricity of gear wheel should be taken into account in a multi-parallel-shaft gear meshing rotor system

Transmission research activities at NASA Lewis Research Center

A joint research program, to advance the technology of rotorcraft transmissions, consists of analytical and experimental efforts to achieve the overall goals of reducing transmission weight and noise, while increasing life and reliability. Recent activities in the areas of transmission and related component research are highlighted. Current areas include specific technologies in support of military rotary wing aviation, gearing technology, transmission noise reduction studies, a recent interest in gearbox diagnostics, and advanced transmission system studies. Results of recent activities are presented along with near term research plans

Vibration Analysis of Gear Mesh using Finite Element Method

Gears are widely used in Machines and Mechanisms. One of the key advantages of gears is having very low fluctuation in speed transmission, but there are several drawbacks also in gears, vibration is one of the main difficulties of gears since load transmission fluctuation is too much high during the meshing of teeth. In this study, motion transfer has been considered between two Involute profile Spur gears mounted on two different shafts. The main objective of the study is to get the frequency of vibration at top node of all four clamps because clamps can be managed by shock-absorbers. One more objective of the study is to obtain the signals of vibration at the top nodes of all four clamps. The analysis is done by using finite element method. “Hunting Tooth Frequency” of gear box has been considered same as rotation frequency of gear box for analysis. Since there are various types of defect also may occur in gear tooth because the tooth is most force bearing elements in the gears, so tooth of gears generally affected by fatigue failures, which generally affect the transmission of motion and power in the gear box. Minor damage in gear teeth profile lead to high chattering, noise and vibration and fluctuation of the load at that particular failure point get increased and at one position, teeth get failed. So for analysis, this case also has been considered for simple spur gear box. A defected tooth has been considered in driving gear. After that having almost same conditions, the analysis is done by the author for defected gearbox also. In results, the amplitude of acceleration at input shaft and at output shaft shown in both cases (with considering X, Y, Z components also) and the result is compared with using the graph with Amplitude of Acceleration and time. Results are verified by comparing “Hunting Tooth Frequency (HTF)” using the analytical method and single sided amplitude spectrum of the gear box

Dynamic Modelling of Power Transmission Systems of Transport Means

The article presents the concept and up to now developed stages of the simulation program for the analysis of dynamic phenomena occurring during the operation of power transmission systems of various means of transport. Currently completed stages of work allow simulation of drive systems with cylindrical gear or planetary gear. The starting points for the implementation of the assumed goal were earlier developed by author considering two independent dynamic models of drive systems with a simple single-stage cylindrical gear and with a planetary gear. Naval and vessel power transmission systems are one example of the fields of application of the developed program. The spread of mechanical propulsion in shipping, which occurred in the nineteenth century, led to different research problems. These include, above all, fuel consumption, which resulted, among others from the efficiency of the entire system. The need to ensure proper performance, avoid unplanned voyage breaks or meet environmental requirements, imposed by increasingly stringent emission standards, results in the search for effective power transmission system solutions and optimization methods for existing ones. One of such methods is dynamic modeling of drive systems, and an example tool that enables the use of this method is the simulation program presented in the article. During development of the concept of the simulation program we admitted the assumption that the model shall enable the determination of dynamic phenomena that occurs in various construction designs of power transmission systems in both - constant and variable conditions of their operation. Thanks to this, the simulation program can be used in two directions of research. The first direction of research is the optimization of newly designed and existing drive systems, and especially the optimization of the construction of toothed gears. It is possible, among others by taking into account the actual, not only assumed, nominal operating conditions. Besides, the dynamic model used by the simulation program allows a wide range of modifications to numerous design features of the system, including the geometry of toothed gear elements. The second direction of research is the development of efficient methods for detecting local damages of system components. Simulation of various combinations of defects in the power transmission system, including damages of gears and bearings, allows also for more effective improvement of present diagnostic algorithms of toothed gears working in power transmission systems of various transport means