Abstract
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.
Highlights
In optimum reducer design, the calculation of the gear ratios of the reducer plays a very important role
Optimal determination of the gear ratios of reducers has been chosen by various researchers in their studies
The gear ratios have been determined for two-stage reducers [1, 2, 3 and 4], three-stage reducers [4, 5, 6, and 8], and four-stage reducers [4, 8, 9 and 10]
Summary
The calculation of the gear ratios of the reducer plays a very important role. There have been a number of optimization studies on determination of gear ratios of helical reducers. For three-stage helical reducers, the gear ratios of the first stage and the second stage can be found from the graph in Figure 1 [1]. The gear ratio of the first stage u1 can be determined from the total ratio uh based on graph in Figure 2 [1]. In [7], [16] and [17], the minimum gearbox length was chosen as the objective of the optimization problem for determining optimum gear ratios. This paper presents a study on the optimal determination of the gear ratios for a two-stage helical reducer in which the objective is the minimal acreage of cross-section
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