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

Reliability based robust design optimization based on sensitivity and elasticity factors analysis

In this paper, a Reliability Based Robust Design Optimization (RBRDO) based on sensitivity and elasticity factors analysis is presented. In the first step, a reliability assessment is performed using the First-and Second Order Reliability Method (FORM)/ (SORM), and Monte Carlo Simulation. Furthermore, FORM method is used for reliability elasticity factors assessment, which can be carried out to determine the most influential parameters, these factors can be help to reduce the size of design variables vector in RBRDO process. The main objective of the RBRDO is to improve both reliability and design of a cylindrical gear pair under uncertainties. This approach is achieved by integration of two objectives which minimize the variance and mean values of performance function. To solve this problem a decoupled approach of Sequential Optimization and Reliability Assessment (SORA) method is implemented. The results obtained shown that a desired reliability with a robust design is progressively achieved

Optimum microgeometry modifications of herringbone gear by means of fitness predicted genetic algorithm

This paper presents a systematic methodology focused on herringbone gear microgeometry modifications toward vibration reduction. The dynamic model considering the unique characteristics of aviation herringbone gear is developed to study the vibration behavior. The optimal ease-off shape can be defined as the outcome of a multi-objective optimization process, the objective functions are loaded transmission error, meshing impact excitation and root mean square (RMS) of vibration acceleration. With special attention given to computational efficiency, a novel fitness predicted genetic algorithm is developed. An application to herringbone gear are presented, the results show the proposed method can obtain optimal modifications that significantly improve the gear performance over a wide range of operating conditions. Furthermore, the reduction of the vibration also leads to a reduction of bending stresses. Finally, a test on herringbone gear is executed under various combinations of torque and speed to demonstrate the accuracy of the proposed model

Transmission error in spur gears: Static and dynamic finite-element modeling and design optimization

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University, 07/10/2010.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 work 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. The work also investigates the main differences between the static and dynamic transmission error generated during the meshing of a spur gear pair model. A combination of Finite-Element Analysis, hybrid numerical/analytical methodology and optimisation algorithms were used to scrutinise the dynamic behaviour of the gear pairs under various operating conditions

Combined misalignments in spur gear transmission systems: a semi-empirical approach

Un área inexplorada en el diseño de sistemas de transmisión de engranajes es el estudio de los efectos de desalineamientos combinados en las medidas de vibración. Actualmente, las investigaciones se centran en desalineamientos individuales y no combinados los cuales reflejan mejor los escenarios de aplicaciones reales. En esta investigación se analizan los efectos de los desalineamientos combinados en las mediciones de vibración en la base de los rodamientos y en el esfuerzo de flexión de los dientes de engranajes rectos de un sistema de transmisión de una etapa. Se diseñó y construyó un banco de pruebas para generar desalineamientos radiales, axiales y angulares en un sistema de transmisión de engranajes de una etapa. Se evaluaron todas las combinaciones posibles de niveles extremos de desalineamiento para un par de engranajes rectos para identificar tendencias en la respuesta vibratoria. Se desarrolló un modelo teórico del área de contacto proyectada para estudiar la relación entre esta y la respuesta vibratoria. Al analizar el cambio en los espectros, se determinó la influencia de diferentes desalineamientos y sus interacciones en las mediciones de vibración. Finalmente, se desarrolló un modelo híbrido para estimar las aceleraciones en los rodamientos, utilizando un modelo de elementos finitos para determinar el esfuerzo de flexión en los dientes y un modelo analítico para estimar las señales de vibración en los rodamientos. El modelo demostró una alta correlación en comparación con los resultados experimentales, validando su efectividad. Finalmente, se propusieron recomendaciones de diseño considerando las zonas de esfuerzo y vibración de interés.DoctoradoDoctor en Ingeniería Mecánic

Reliability based robust design optimization based on sensitivity and elasticity factors analysis

In this paper, a Reliability Based Robust Design Optimization (RBRDO) based on sensitivity and elasticity factors analysis is presented. In the first step, a reliability assessment is performed using the First-and Second Order Reliability Method (FORM)/ (SORM), and Monte Carlo Simulation. Furthermore, FORM method is used for reliability elasticity factors assessment, which can be carried out to determine the most influential parameters, these factors can be help to reduce the size of design variables vector in RBRDO process. The main objective of the RBRDO is to improve both reliability and design of a cylindrical gear pair under uncertainties. This approach is achieved by integration of two objectives which minimize the variance and mean values of performance function. To solve this problem a decoupled approach of Sequential Optimization and Reliability Assessment (SORA) method is implemented. The results obtained shown that a desired reliability with a robust design is progressively achieved

Tribo-dynamic analysis of hypoid gears in automotive differentials

Torsional vibrations in differentials of Rear Wheel Drive vehicles are of major importance for the automotive industry. Hypoid transmissions, forming the motion transfer mechanism from the driveshaft to the wheels, suffer from severe vibration issues. The latter are attributed to improper mesh between the mating gear flanks due to misalignments, variation of contact load and shifting of the effective mesh position. For certain operating conditions, the gear pair exhibits high amplitude motions accompanied with separation of the mating surfaces. Ultimately, single or even double-sided vibro-impact phenomena evolve, which have been related to noise generation. This thesis attempts to address these issues by effectively analysing the dynamic behaviour of a hypoid gear pair under torsional motion. The case study considered is focused on a commercial light truck. The major difference of the employed mathematical model to prior formulations is the usage of an alternative expression for the dynamic transmission error so that the variation of contact radii and transmission error can be accounted for. This approach combined to a correlation of the resistive torque in terms of the angular velocity of the differential enables the achievement of steady state, stable periodic solutions. The dynamic complexity of systems with gears necessitates the identification of the various response regimes. A solution continuation method (software AUTO) is employed to determine the stable/unstable branches over the operating range of the differential. The ensuing parametric studies convey the importance of the main system parameters on the dynamic behaviour of the transmission yielding crucial design guidelines. A tribo-dynamic investigation aims at expanding the dynamic model from pure dry conditions to a more integrated elastohydrodynamic (EHL) approach. Analytical and extrapolated solutions are applied for the derivation of the film thickness magnitude based on the kinematic and loading characteristics of the dynamic model. The temperature rise is governed mainly by conduction due to the thin lubricant films. The generated friction is also computed as a function of the viscous shear and asperity interactions. The effective lubricant viscosity is greatly affected by the pressure increase due to the resonant behaviour of the contact load. The final part of this work is involved with a feasibility study concerning the application of Nonlinear Energy Sinks (NES) as vibration absorbers, exploiting their ability for broadband frequency interaction. Response regimes associated with effective energy absorption are identified and encouraging results are obtained, showing the potential of the method

Automated topology optimisation of hybrid electric vehicle powertrains

Ing, A. H., & McPhee, J. (2015). Automated topology optimisation of hybrid electric vehicle powertrains. International Journal of Electric and Hybrid Vehicles, 7(4), 342. Final version published by Inderscience Publishers, and available at: https://doi.org/10.1504/IJEHV.2015.074671Gasoline and electric powertrain components can be connected in numerous configurations to create hybrid powertrains. Owing to the exponential increase of permutations as the number of components increases, a framework to determine the best possible powertrain configuration that minimises fuel consumption was developed. This framework uses enumeration to discover all powertrains, the Graph-Theoretic Method to generate system equations, dynamic programming to evaluate fuel consumption and generate an objective score, and Pattern Search to optimise the sizing of each component. A multi-stage screening process was used to reduce computation time. Parallel and powersplit-like topologies with additional discrete gearboxes were found to be the most efficient. The best performing topology is a powersplit hybrid type: a discrete gearbox connected to the final drive, with the output gear of the planetary carrier and electric motor in parallel.The project is funded by Toyota, Maplesoft, and NSERC

Transmission error in spur gears : static and dynamic finite-element modeling and design optimization

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 work 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. The work also investigates the main differences between the static and dynamic transmission error generated during the meshing of a spur gear pair model. A combination of Finite-Element Analysis, hybrid numerical/analytical methodology and optimisation algorithms were used to scrutinise the dynamic behaviour of the gear pairs under various operating conditions.EThOS - Electronic Theses Online ServiceGBUnited Kingdo