Pitting damage levels estimation for planetary gear sets based on model simulation and grey relational analysis

The planetary gearbox is a critical mechanism in helicopter transmission systems. Tooth failures in planetary gear sets will cause great risk to helicopter operations. A gear pitting damage level estimation methodology has been devised in this paper by integrating a physical model for simulation signal generation, a three-step statistic algorithm for feature selection and damage level estimation for grey relational analysis. The proposed method was calibrated firstly with fault seeded test data and then validated with the data of other tests from a planetary gear set. The estimation results of test data coincide with the actual test records, showing the effectiveness and accuracy of the method in providing a novel way to model based methods and feature selection and weighting methods for more accurate health monitoring and condition prediction

Dynamics of a split torque helicopter transmission

A high reduction ratio split torque gear train has been proposed as an alternative to a planetary configuration for the final stage of a helicopter transmission. A split torque design allows a high ratio of power-to-weight for the transmission. The design studied in this work includes a pivoting beam that acts to balance thrust loads produced by the helical gear meshes in each of two parallel power paths. When the thrust loads are balanced, the torque is split evenly. A mathematical model was developed to study the dynamics of the system. The effects of time varying gear mesh stiffness, static transmission errors, and flexible bearing supports are included in the model. The model was demonstrated with a test case. Results show that although the gearbox has a symmetric configuration, the simulated dynamic behavior of the first and second compound gears are not the same. Also, results show that shaft location and mesh stiffness tuning are significant design parameters that influence the motions of the system

Vibration in Planetary Gear Systems with Unequal Planet Stiffnesses

An algorithm suitable for a minicomputer was developed for finding the natural frequencies and mode shapes of a planetary gear system which has unequal stiffnesses between the Sun/planet and planet/ring gear meshes. Mode shapes are represented in the form of graphical computer output that illustrates the lateral and rotational motion of the three coaxial gears and the planet gears. This procedure permits the analysis of gear trains utilizing nonuniform mesh conditions and user specified masses, stiffnesses, and boundary conditions. Numerical integration of the equations of motion for planetary gear systems indicates that this algorithm offers an efficient means of predicting operating speeds which may result in high dynamic tooth loads

Expansion of epicyclic gear dynamic analysis program

The multiple mesh/single stage dynamics program is a gear tooth analysis program which determines detailed geometry, dynamic loads, stresses, and surface damage factors. The program can analyze a variety of both epicyclic and single mesh systems with spur or helical gear teeth including internal, external, and buttress tooth forms. The modifications refine the options for the flexible carrier and flexible ring gear rim and adds three options: a floating Sun gear option; a natural frequency option; and a finite element compliance formulation for helical gear teeth. The option for a floating Sun incorporates two additional degrees of freedom at the Sun center. The natural frequency option evaluates the frequencies of planetary, star, or differential systems as well as the effect of additional springs at the Sun center and those due to a flexible carrier and/or ring gear rim. The helical tooth pair finite element calculated compliance is obtained from an automated element breakup of the helical teeth and then is used with the basic gear dynamic solution and stress postprocessing routines. The flexible carrier or ring gear rim option for planetary and star spur gear systems allows the output torque per carrier and ring gear rim segment to vary based on the dynamic response of the entire system, while the total output torque remains constant

Effect of planetary gearboxes on the dynamics of rotating systems

The coupled dynamic behaviour of planetary geared rotor systems is much less well understood compared to the classical geared rotor systems. For a better understanding, this research project investigates the coupled dynamic behaviour of planetary geared rotor systems and how the planetary gearbox parameters affect their global dynamics. In the numerical study, a six degrees of freedom hybrid dynamic model of a planetary geared rotor system is created in the recently developed “GEAROT” rotor dynamics software by considering gyroscopic effects. Based on the modal analysis results of the hybrid dynamic model, the vibration modes are classified as coupled torsional-axial, lateral and gearbox for the helical gear configuration, and torsional, axial, lateral and gearbox for the spur one. Modal energy analysis is used to quantify the coupling level between the shafts and planetary gearbox, which highlights the effect of a planetary gearbox on the dynamic behaviour of a rotating system. An extensive planetary gearbox parameter study including gear contact, gearbox mass and support, and planet gear parameters is conducted using the hybrid dynamic model to investigate the parameter effects on the modal behaviour of planetary geared rotors. The sensitivity of planetary geared rotor vibration modes to the gearbox parameters is determined by computing the frequency shifts and comparing the mode shapes between the two extreme cases. In the experimental study, free-free impact hammer tests are carried out on a planetary geared rotor assembly to validate the numerical modal analyses results in “GEAROT”. On the basis of both experimental and numerical modal analysis of planetary geared rotors, the lateral vibration modes are identified as “in phase” and “out of phase”. Briefly, the numerically identified lateral modal behaviour of planetary geared rotor systems is successfully validated with the experimental modal analysis results.Open Acces

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

Modal analysis of multistage gear systems coupled with gearbox vibrations

An analytical procedure to simulate vibrations in gear transmission systems is presented. This procedure couples the dynamics of the rotor-bearing gear system with the vibration in the gear box structure. The model synthesis method is used in solving the overall dynamics of the system, and a variable time-stepping integration scheme is used in evaluating the global transient vibration of the system. Locally each gear stage is modeled as a multimass rotor-bearing system using a discrete model. The modal characteristics are calculated using the matrix-transfer technique. The gearbox structure is represented by a finite element models, and modal parameters are solved by using NASTRAN. The rotor-gear stages are coupled through nonlinear compliance in the gear mesh while the gearbox structure is coupled through the bearing supports of the rotor system. Transient and steady state vibrations of the coupled system are examined in both time and frequency domains. A typical three-geared system is used as an example for demonstration of the developed procedure

Dynamics-Based Vibration Signal Modeling for Tooth Fault Diagnosis of Planetary Gearboxes

Vibration analysis has been widely used to diagnose gear tooth fault inside a planetary gearbox. However, the vibration characteristics of a planetary gearbox are very complicated. Inside a planetary gearbox, there are multiple vibration sources as several sun-planet gear pairs, and several ring-planet gear pairs are meshing simultaneously. In addition, due to the rotation of the carrier, distance varies between vibration sources and a transducer installed on the planetary gearbox housing. Dynamics-based vibration signal modeling techniques can simulate the vibration signals of a planetary gearbox and reveal the signal generation mechanism and fault features effectively. However, these techniques are basically in the theoretical development stage. Comprehensive experimental validations are required for their future applications in real systems. This chapter describes the methodologies related to vibration signal modeling of a planetary gear set for gear tooth damage diagnosis. The main contents include gear mesh stiffness evaluation, gear tooth crack modeling, dynamic modeling of a planetary gear set, vibration source modeling, modeling of transmission path effect due to the rotation of the carrier, sensor perceived vibration signal modeling, and vibration signal decomposition techniques. The methods presented in this chapter can help understand the vibration properties of planetary gearboxes and give insights into developing new signal processing methods for gear tooth damage diagnosis