Eventos Anais de eventos
COBEM 2023
27th International Congress of Mechanical Engineering
PARAMETER ESTIMATION OF A SINGLE STAGE GEARBOX USING THE LEVENBERG-MARQUARDT METHOD
Submission Author:
Tobias Rosa , RJ , Brazil
Co-Authors:
Tobias Rosa, Bruna Loiola, Elias Dias Rossi Lopes, Gustavo Simão Rodrigues
Presenter: Tobias Rosa
doi://10.26678/ABCM.COBEM2023.COB2023-0686
Abstract
The vehicle transmission system is responsible for transmitting mechanical energy from the engine to the driving wheels. In order to improve the safety and performance of the vehicle, advanced control techniques have been applied for the most diverse subsystems, including the powertrain. The control is based on the mathematical modeling of the dynamic behavior of the vehicle and it may be considered for the longitudinal, lateral, or vertical dynamics. The transmission system is part of the longitudinal dynamics and influences the performance and safety of the vehicle. A transmission system can be subdivided into other geared pair subsystems, including pre-reduction and post-reduction. The mathematical model of a pair of gears is obtained analytically using Newton-Euler equations of motion resulting in a system of equations with four degrees of freedom and includes the definition of parameters such as inertia, damping, and stiffness, which are often unknown. Therefore, under these circumstances, the present work uses the concept of inverse problems to estimate the parameters of the dynamic model of a pair of gears, using the Levenberg-Marquardt (LM) method. Firstly, the sensitivity analysis is performed and indicates that it is possible to estimate the gearing stiffness, shaft damping coefficient, and gearing damping coefficient at the same time. Besides that, to initialize the LM algorithm, synthetic measurements of the angular position of the input and output gears are necessary, in addition to an approximation of the parameters. Aiming to demonstrate the effectiveness of the method, the algorithm is initialized with inaccurate values for the estimated parameters to verify if the method is capable of converging to the correct values of the parameters. Moreover, the algorithm is evaluated with noisy simulated data and different initial conditions, so that the robustness of the proposed method is demonstrated. The results show that the responses of the dynamic model with the estimated parameters are accurate, compared with the original data.
Keywords
gear pair, Dynamic model, Levenberg-Marquardt method, Inverse problem, Numerical simulation
