<p style="text-align: center;"><img src="/ueditor/php/upload/image/20251023/1761206592651544.png" title="1761206592651544.png" alt="4.png"/></p><p style="text-align: justify;"><span style="font-family: arial, helvetica, sans-serif; font-size: 12px;">Asymmetric tooth gears are not standardized, which enables the optimization of virtually any combination of gear tooth geometry parameters. However, the specific optimization goals are determined by the intended application and the performance priorities of the gear drive system. In high-performance applications, such as automotive gearboxes, minimizing stress at the gear tooth root becomes a critical design objective. The Direct Gear Design methodology incorporates a tooth root optimization approach developed by Dr. Yuriy Shekhtman. This technique employs two-dimensional finite element analysis (FEA) using linear triangular elements for stress calculations. It is integrated with a random search algorithm to facilitate multiparametric iterations throughout the optimization process. The method utilizes trigonometric, polynomial, and exponential functions to accurately define the optimized root profile. As demonstrated in Figure 4, asymmetric tooth root optimization results in a uniform distribution of tensile and compressive bending stresses along the root profile, leading to a significant reduction in peak root stress values.</span></p>