This article introduces a study on the optimal calculation of gear ratios of a two-stage helical reducer. In the study, the acreage of the cross section of the reducer was chosen as the objective function of the optimization problem. Also, the design equation for pitting resistance of a gear set was investigated. Furthermore, the equations on moment equilibrium condition of a two-stage helical reducer and their regular resistance condition were analysed. A computer program was performed to determine the optimal partial transmission ratios for getting the minimal acreage of the cross section of the system. From the results of the computer program, two models for determining the optimal gear ratios of a two-stage reducer were proposed. Using these models, the gear ratios can be calculated accurately in a simple way.

This paper presents a new study on optimum calculation of partial ratios of three-step helical gearboxes. The chosen objective function is the cross section dimension of the gearbox. In solving the optimization problem, the design equation for pitting resistance of a gear set was investigated and equations on moment equilibrium condition of a mechanic system including three gear units and their regular resistance condition are analyses. From the results of the study, effective formula for determination of the partial ratios of three-step helical gearboxes is introduced. As the formulas are explicit, the partial ratios can be calculated accurately and simply.

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This paper presents a study on the determination of the optimum gear ratios of a two-stage helical reducer with first stage double gear sets. In the study, an optimization problem was built in order to find the optimum gear ratios of the reducer. In the optimization problem, the objective function was the reducer cross section area. Also, the influence of the input factors including the total reducer ratio, the wheel face width coefficient, the allowable contact stress and the output torque were evaluated. In order to investigate the effects of these factors on the optimum gear ratios, a simulation experiment was designed and conducted. In addition, equations for calculating the optimum gear ratios were introduced. By using these equations, the gear ratios can be determined accurately in a simple way.