Gear Design Multi-Objective Optimization for Automotive Transmissions
Examensarbete för masterexamen
Automotive engineering (MPAUT), MSc
Bhat, Akshay Daila Subramanya
Transmission design and development have to take a lot of design variables and their resulting eﬀects into account as early in the design stage as possible. Most of these resulting eﬀects(also known as objective functions in this thesis) are conﬂicting in nature. There will be an optimal set of design variables that will result in minimum or maximum of these objective functions. It is very beneﬁcial to arrive at this optimal set of design variables using a structured methodology rather than trial and error methods to obtain unique solutions and save time. Gear whine and durability are the two main conﬂicting factors considered in this thesis. The optimization methodology which is the aim of this thesis, is built to minimize the peak-peak transmission error, contact and root stresses by modifying the micro-geometry variables. The thesis was performed in collaboration with CEVT AB. A design space is selected for the micro-geometry variables. WindowsLDP, a software used for gear tooth contact analysis ,is used for Design of Experiments(DOE) to calculate the objective functions for multiple design points within the design space. Probability distribution and worst-case scenario distribution is applied for the objective functions to make them robust against torque. The data is then used to develop metamodels for each objective function in MATLAB using squared exponential Gaussianr egression. They are then used in a multi-objective optimization algorithm in MATLAB to explore the design space and obtain a pareto/non-dominated set of solutions. These solutions are checked for design safety and ranked highest to lowest based on weights distributed between peak-peak transmission error and safety factors. The highest ranked micro-geometry values are substituted in the original gear model and the objective functions are calculated against torque and compared to the benchmark. The highest ranked pareto optimal result shows that peak-peak transmission error, contact stress and gear 2 root stress minimized compared to the benchmark although there was a slight increase in gear 1 root stress. Other pareto optimal solutions show diﬀerent levels of minimization for diﬀerent objective functions. But this is normal as the objective functions are conﬂicting to each other. Also, once the design safety conditions are satisﬁed, reducing the peak-peak transmission error and hence the gear whine is very important. Based on the results obtained, it can be concluded that the developed methodology managed to optimize the micro-geometry variables to minimize the objective functions in a very structured format and minimal time. It also arrived at a unique set of pareto solutions every time the optimization was completed, given that the conditions remained the same.
micro-geometry , peak-peak transmission error , contact stress , root stress , metamodel , robustness measure , optimization