# Influence of Open Differential Design on the Mass Reduction Function
## 1 Introduction
### Mass Reduction Impact on Improving Energy Efficiency  
Vehicles with internal combustion engines significantly pollute the environment. EU energy policy resulted in directive 2012/27/EU [9], which encourages the implementation of energy efficiency measures in member countries. In order to improve energy efficiency, special attention is dedicated to traffic, which is reflected in the guidelines EN 16247-4:2022 [10]. By reducing the mass of the vehicle, it contributes to the reduction of fuel consumption and in this way to the improvement of the energy efficiency of the vehicle. Differential transmissions, due to their design performance and the choice of material from which they are made (gray cast iron), have an increased mass, which contributes to the overall increase in the mass of the vehicle. Therefore, certain research papers deal with the selection of materials for making gears, analyzing the behavior of the differential at different rotation speeds, different gear mesh frequencies and different natural frequencies [11]. Selection of materials, such as composite materials [12; 13], or gearboxes with gears made from polymer materials [14], has an impact on the mass reduction of the transmission, corrosion resistance, less abrasive wear and improved energy efficiency. By varying different print densities when producing gears from Acrylonitrile Butadiene Styrene (ABS), it is possible to obtain gears of lower mass with lower print densities (60% ABS density), while the stresses in the gears meet the permitted stresses [15]. In this way, the mass reduction of the design elements of the differential transmissions contributes to the overall mass reduction of the vehicles. According to [16], it is necessary to develop transmissions with an increase in their efficiency, in order to reduce fuel consumption. By mass increasing the design elements of the differential transmission, the consumption of materials required for their production increases, and at the same time it reduces fuel efficiency [16]. Through the analysis of oil distribution at the different conditions with hypoid gears [17], an increase in the degree of useful action of the transmission is achieved, i.e., a reduction in power losses in the transmission. Papers [18; 19], using the volume of fluid (VOF) method and computational fluid dynamics (CFD), analyze the influence of the speed factor, oil viscosity and immersion depth on the churning losses of spur gears. The application of multi-objective optimization methods in the development and improvement of new design solutions is significant [20]. Thus, the improvement of transmission efficiency is achieved by optimizing the geometry of the transmission, which affects the strength of the gear's teeth, noise reduction, vibration reduction and better power transmission [21; 22]. Changing the micro and macro geometry of the gear teeth affects the transmission error and its reduction [22]. Macro geometry affects the change of the gear tooth profile in the axial direction and the tooth surface direction by the intentional removal of material from the gear teeth flanks [21]. Optimizing the parameters of the macro geometry affects the volume of the gear teeth, i.e., the reduction and increase in its mass [23]. Research in papers [24; 25] analyzes the influence of micro geometry change on tooth strength. [PERSON] and [PERSON] [26], using the Artificial Immune System (AIS) algorithm, analyzed design parameters that have the greatest impact on the mass and volume reduction of the planetary gear train. By applying the AIS algorithm, they optimized the volume of the planetary gear train. Research [27] proposed a machine learning method in the design of non-involuted gears. With this method, predicted parameter \(Y_{\mathrm{Z}}\) and nominal gear root stress were proposed. This is important from the aspect of increasing the accuracy of the gear calculation and gear optimization. Authors in [28] analyze the influence effects of center distance deviation on polymer gearbox life.