Design Optimization of Gear Transmission System with Nonlinear Properties

Christos Theodosiou

Stavroula Stefanatou, Johannes Heydenreich
PhilonNet Engineering Solutions

The current work presents a seamless design and optimization procedure of gear transmission systems subjected in dynamic loading. First, a nonlinear mathematical model of a gear-pair system supported on bearings with rolling elements is introduced. In this model, the housing of the gearbox is modeled by using finite elements, while the essential effects of the gear-pair, the bearings and the shafts are taken into account via a nonlinear modeling. The equations that describe the behavior of this nonlinear model have been introduced in a specially designed compact element. This new gear-pair force element is included in the latest version of Dynamis solver. It possesses strongly nonlinear characteristics, accounting for gear backlash, meshing stiffness, transmission error properties and bearing stiffness nonlinearities. Finally, the gearbox with the gear-pair system is optimized for low noise emissions and low bearing forces in the working frequency range. The dynamic behavior of the mechanical system using different characteristics of the gear-pair properties is investigated. A multi-objective and multi-disciplinary optimization is performed using modeFRONTIER, with input parameters such as meshing stiffness amplitude and variation, backlash properties and output parameters such as acceleration on selected points of the gearbox surface and forces on the bearings. The seamless coupling between modeFRONTIER and Dynamis enabled the automation of the design and simulation process. The Multilevel Dynamic Substructuring Method (MLDS) of Dynamis enabled the use a high accuracy fine-mesh gearbox model. The MLDS method delivers a residual structure that possesses drastically smaller size, without sacrificing numerical accuracy. This increases the efficiency and speed of dynamical computation and facilitates multiple design evaluations during optimization.