Optimum Determination of Partial Transmission Ratios of Three-Step Helical Gearboxes for Getting Minimum Cross Section Dimension

Abstract

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.

Multi-Objective Optimization of a Two-Stage Helical Gearbox Using Taguchi Method and Grey Relational Analysis

“…Various objective functions are utilized to solve the single-objective optimization problem of determining the optimal gear ratio of helical gearboxes. These objective functions include minimizing gearbox length [4][5][6][7], minimizing gearbox cross section area [6,[8][9][10], minimizing gearbox mass [6,11], minimizing gearbox volume [12], and minimizing gearbox cost [13][14][15][16]. All of these studies share a common feature in that only one design parameter, the partial gear ratio, is defined in the form of an explicit model.…”

Cost optimization of two-stage helical gearboxes with second stage double gear-sets

“…Relation between gear mass and gear ratio of second stage [1] Up to now, the optimal gear ratio of a gearbox has been determined using various methods such as using graphs [2,3], using «practical formulas» [4] which have been found based on the results from gearbox companies, or using optimal models [5,6]. In addition, the problem of calculating the optimal gear ratio has been performed for different types of gearboxes such as helical gear boxes [6][7][8], bevel gear boxes [9][10][11], worm gearboxes [12][13][14][15]. Besides, the optimal gear ratios have been determined for two-stage [7,8,14], three-stage [6,10,11], and four-stage gearbo xes [16,17].…”

“…In addition, the problem of calculating the optimal gear ratio has been performed for different types of gearboxes such as helical gear boxes [6][7][8], bevel gear boxes [9][10][11], worm gearboxes [12][13][14][15]. Besides, the optimal gear ratios have been determined for two-stage [7,8,14], three-stage [6,10,11], and four-stage gearbo xes [16,17]. Also, different objectives have also been selected when solving this problem such as the minimum mass of gears [16,18], minimum mass of gearbox [19], the minimum gearbox cross-section section [8,10,14], the minimum gearbox length [17,20], or minimum gearbox cost [9,21].…”

Determining Optimal Gear Ratios of a Two-stage Helical Reducer for Getting Minimal Acreage of Cross Section

“…There have been quite a lot of studies which follow this method. In [5] and [14], the gear ratios were found in order to get the minimal cross section dimension of the gearbox. In [6], [9], [10] and [15], the objective for optimization problem was the minimum mass of gears.…”

“…In [5] and [14], the gear ratios were found in order to get the minimal cross section dimension of the gearbox. In [6], [9], [10] and [15], the objective for optimization problem was the minimum mass of gears. In [7], [16] and [17], the minimum gearbox length was chosen as the objective of the optimization problem for determining optimum gear ratios.…”