Volume Optimization of Two-Stage Helical Gear Train using Differential Evolution Algorithm



  • Vikash Kumar Department of Mechanical Engineering, Indian Institute of Technology Patna, Bihta 801 106, Bihar, India
  • Sachin Kumar Singh Department of Mechanical Engineering, Indian Institute of Technology (ISM) Dhanbad, Dhanbad 826 004, Jharkhand, India




Design optimization, Design parameters, Dynamic penalty function, Gear parameters, Power transmission


In high-performance power transmission systems like automotive and aerospace, the proper gear train design is essential because it requires minimum weight and high-efficiency gearboxes with maximum service life. An iterative design method that takes into account all viable design options is used to achieve the desired outcome. This procedure cannot be automated using the traditional methods utilized in its design. As a result, this paper makes an attempt to automate the gear train's preliminary design. This paper uses the Differential Evolution (DE) optimization technique and a dynamic penalty function to optimize the two-stage helical gear train's design parameters by minimising the objective function i.e., the gear train's overall geometrical volume (size). The objective function is constrained by bending force, surface fatigue strength, and interference equations of helical gear train with the design variables such as number of teeth, face width, module, and helix angle of each gear. Ranges of design parameters are taken from the manufacturer's catalogue. The optimised design parameters obtained from the proposed approach are compared and validated with the standard gear parameters (i.e., catalogue value) and with the results published in the literature applying other optimising approaches such as Genetic Algorithm (GA) and Fminsearch Solver (FS). The proposed approach shows a significant reduction i.e., 18.51% with GA and 18.14% with FS in the overall geometrical volume (size) of the two-stage helical gear train as compared to the published work. The presented approach enhances the design optimization problem of gear train which may be used in automobile, aircrafts, and robotics application for optimal performance.