Global dynamic modeling of a transmission system

The work performed on global dynamic simulation and noise correlation of gear transmission systems at the University of Akron is outlined. The objective is to develop a comprehensive procedure to simulate the dynamics of the gear transmission system coupled with the effects of gear box vibrations. The developed numerical model is benchmarked with results from experimental tests at NASA Lewis Research Center. The modal synthesis approach is used to develop the global transient vibration analysis procedure used in the model. Modal dynamic characteristics of the rotor-gear-bearing system are calculated by the matrix transfer method while those of the gear box are evaluated by the finite element method (NASTRAN). A three-dimensional, axial-lateral coupled bearing model is used to couple the rotor vibrations with the gear box motion. The vibrations between the individual rotor systems are coupled through the nonlinear gear mesh interactions. The global equations of motion are solved in modal coordinates and the transient vibration of the system is evaluated by a variable time-stepping integration scheme. The relationship between housing vibration and resulting noise of the gear transmission system is generated by linear transfer functions using experimental data. A nonlinear relationship of the noise components to the fundamental mesh frequency is developed using the hypercoherence function. The numerically simulated vibrations and predicted noise of the gear transmission system are compared with the experimental results from the gear noise test rig at NASA Lewis Research Center. Results of the comparison indicate that the global dynamic model developed can accurately simulate the dynamics of a gear transmission system

Nonlinear behavior of a spur gear pair transmission system with backlash

In order to investigate the nonlinear characteristics of gear transmission system under the action of external and internal excitations, a dynamic model of a spur gear pair was established involving the backlash, damping, transmission error and the meshing stiffness. Based on the incremental harmonic balance method (IHBM), the general forms of the periodic solution with arbitrary precision are deduced. The vibration response obtained by IHBM compare very well with the results obtained by New-Mark method, which verifies the accuracy and electiveness of the analytical methodology (IHBM) and provide information on the dynamic characteristic of spur gear. The simulation results revealed that several types of steady-state periodic solution are identified and determined by employing the IHBM. Due to the effect of backlash, the nonlinear characteristics of jump discontinuity phenomena and multiple stable solutions coexist and the meshing impact phenomenon are obvious. In addition, the influences of the system damping, transmission error and excitation amplitude on the amplitude frequency characteristic are illustrated by a series of diagrams. The results implicate that increasing the external excitation amplitude and system damping can effectively decrease the system resonant amplitude and control the nonlinear vibration response of the gear system and the effect of hardening spring behavior becomes weaker. The transmission error excitation amplitude variation also tends to worse the degree of nonlinearity. Therefore, it presents some useful information to reduce the vibration and noise of gear system

Vibration and noise analysis of a gear transmission system

This paper presents a comprehensive procedure to predict both the vibration and noise generated by a gear transmission system under normal operating conditions. The gearbox vibrations were obtained from both numerical simulation and experimental studies using a gear noise test rig. In addition, the noise generated by the gearbox vibrations was recorded during the experimental testing. A numerical method was used to develop linear relationships between the gearbox vibration and the generated noise. The hypercoherence function is introduced to correlate the nonlinear relationship between the fundamental noise frequency and its harmonics. A numerical procedure was developed using both the linear and nonlinear relationships generated from the experimental data to predict noise resulting from the gearbox vibrations. The application of this methodology is demonstrated by comparing the numerical and experimental results from the gear noise test rig

Dynamic simulation analysis of spur gear space driven system with large inertia load

The wide application of large inertia loads in space drive mechanisms is relatively rare in theoretical research. An 8-degree-of-freedom nonlinear dynamic model is established for the time-varying and nonlinear perturbation problems of a large inertia load space drive mechanism. The model is a two-stage spur gear model in which the effects of backlash and time-varying stiffness are considered. The 3D model was imported into ADAMS, and the nonlinear dynamic response of the system was studied by motion simulation. This paper sets up a large inertia experimental device to collect and process data. Comparing experimental results with Adams results, the correctness of the numerical model was verified, and the reasons for the differences between the two were explained. A comparative analysis of the load response under different inertia was performed to illustrate the importance of studying large inertia loads. The simulation results show that the output shaft has a great influence on the dynamic response. Changing the material of the gear can improve the transmission precision of the gear system. The analysis results in this paper enrich the research on the dynamic response of gear system, and provide a theoretical basis for the subsequent design of large inertia load gear system and improve vibration and noise during operation

Analytical and experimental study of vibrations in a gear transmission

An analytical simulation of the dynamics of a gear transmission system is presented and compared to experimental results from a gear noise test rig at the NASA Lewis Research Center. The analytical procedure developed couples the dynamic behaviors of the rotor-bearing-gear system with the response of the gearbox structure. The modal synthesis method is used in solving the overall dynamics of the system. Locally each rotor-gear stage is modeled as an individual rotor-bearing system using the matrix transfer technique. The dynamics of each individual rotor are coupled with other rotor stages through the nonlinear gear mesh forces and with the gearbox structure through bearing support systems. The modal characteristics of the gearbox structure are evaluated using the finite element procedure. A variable time steping integration routine is used to calculate the overall time transient behavior of the system in modal coordinates. The global dynamic behavior of the system is expressed in a generalized coordinate system. Transient and steady state vibrations of the gearbox system are presented in the time and frequency domains. The vibration characteristics of a simple single mesh gear noise test rig is modeled. The numerical simulations are compared to experimental data measured under typical operating conditions. The comparison of system natural frequencies, peak vibration amplitudes, and gear mesh frequencies are generally in good agreement

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

Reduction of gear pair transmission error with tooth profile modification

The gear noise problem that widely occurs in power transmission systems is typically characterised by one or more high amplitude acoustic signals. The noise originates from the vibration of the gear pair system caused by transmission error excitation that arises from tooth profile errors, misalignment and tooth deflections. This paper aims to further research the effect of tooth profile modifications on the transmission error of gear pairs. A spur gear pair was modelled using finite elements, and the gear mesh was simulated and analysed under static conditions. The results obtained were used to study the effect of intentional tooth profile modifications on the transmission error of the gear pair. A detailed parametric study, involving development of an optimisation algorithm to design the tooth modifications, was performed to quantify the changes in the transmission error as a function of tooth profile modification parameters as compared to an unmodified gear pair baseline

Modelling of 4WD vehicle driveability during tip-in/tip-out events

This paper describes a modelling method to investigate the dynamic behaviour of 4WD vehicle under a severe driving condition, where the driver applies a rapid tip-in on the accelerator pedal in 2nd gear to achieve maximum engine torque. This is followed by a tip-out event by releasing the accelerator quickly. The Tip-In/Tip-Out events are one of important elements to assess the vehicle driveability. During these test events, the vehicle is expected to generate low frequency vibration between 2 Hz and 10 Hz and gives discomfort feelings induced by resonance effects on sensitive human organs. The aim of this paper is to develop a 4WD vehicle model in a modern object-oriented multi-body simulation tool and study its driveability

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