# Influence of Open Differential Design on the Mass Reduction Function
## 7 Conclusions  
ODT, due to its relatively simple design, is installed in road vehicles with rear drive, in order to achieve the transmission of power and motion from the driving machine to the vehicle's wheels. Due to its robust (massive) structural performance, it has the effect of increasing the mass of the road vehicles in which it is installed. As the mass of the vehicle increases, the consumption of fossil fuels increases and the energy efficiency of internal combustion engine vehicles decreases. Therefore, the goal of the research presented in this paper is to propose an algorithm that, by combining FEM, TOM and RSM, allows finding design parameters for the two design elements (ring gear and drive shaft with pinion) whose optimization reduces the overall mass of the ODT. The emphasis is placed on finding design parameters that are not part of the micro and macro parameters of gears, but are general design parameters that must be found for both gears and ODT shafts. Figure 19: Distribution of equivalent von Mises stresses on ring gear. Figure 20: Mass comparison of the design elements of the differential transmission before and after optimization. According to ISO 23509:2006, an analytical calculation of ODT was performed. By applying FEM static analysis, an initial numerical calculation of the displacements and equivalent stresses according to von Mises was performed for the ring gear and the drive shaft with pinion. Using the submodeling method (global-local FEM approach), the amounts of the maximum equivalent stresses of the teeth in the engagement of the pinion and ring gear were obtained. After comparing the obtained numerical results with the results of the analytical calculation of stress at the tooth root and Hertzian stress at the tooth face flank, the validity of the numerical model was confirmed. Also, the amounts of the displacements and maximum equivalent stresses according to von [PERSON] were obtained by the numerical calculation of the drive shaft with pinion. From the initial calculation of the drive shaft using FEM analysis, due to the low values of the maximum equivalent stresses according to von Mises, one design parameter of the internal radius (\(r\)) is proposed as input parameters for the analysis by the RSM. The remaining three design parameters (\(a\), \(b\) and \(h\)) were obtained by topological optimization of the ring gear. By applying the RSM, a mathematical model described by three mathematical equations was developed. Through the mentioned equations, the influence of the mentioned four design parameters on the three response variables was analyzed. Using the obtained equations, three objective functions are described: mass reduction of the optimized design elements (\(m_{\text{all}}\)), mass reduction of the ring gear (\(m_{1}\)) and mass reduction of the drive shaft (\(m_{2}\)). From the local sensitivity analysis, the parameters of the inner radius of the drive shaft (\(r\)) and overhang height of the ring gear (\(h\)) have the greatest influence on the \(m_{\text{all}}\) response variable. Then, we followed the parameters vertical and horizontal chamfer of the ring gear (\(a\) and \(b\)). Based on the partial objective functions of mass reduction of each optimized design element (\(m_{1}\) and \(m_{2}\)), a significant influence of the selected design parameters on this design element can be seen. All ring gear parameters \(h\), \(b\) and \(a\) have influence on objective function \(m_{1}\) where parameter \(h\) is dominant. This is visible through the obtained mathematical Equation (40). The parameter \(r\) has the largest effect on the function \(m_{2}\). By choosing general design parameters and analyzing their influence using the obtained mathematical model, it was possible to create a new geometry of the ring gear and drive shaft with pinion. After the optimization, the overall mass of the optimized design elements was reduced by 16.5% compared to the mass of the same elements before optimization with the proposed algorithm.