| Summary: | This study is aimed at determining optimum partial gear ratios to minimize the cost of a three-stage helical gearbox. In this work, eleven input parameters were investigated to find their influence on the optimum gear ratios of the second and the third stages (<inline-formula> <math display="inline"> <semantics> <mrow> <msub> <mi>u</mi> <mn>2</mn> </msub> </mrow> </semantics> </math> </inline-formula> and <inline-formula> <math display="inline"> <semantics> <mrow> <msub> <mi>u</mi> <mn>3</mn> </msub> </mrow> </semantics> </math> </inline-formula>). To reach the goal, a simulation experiment was designed and implemented by a cost optimization program. The results revealed that in addition to the input parameters, their interactions also have important effects in which the total ratio gearbox ratio (<inline-formula> <math display="inline"> <semantics> <mrow> <msub> <mi>u</mi> <mi>t</mi> </msub> </mrow> </semantics> </math> </inline-formula>) and the cost of shaft (<inline-formula> <math display="inline"> <semantics> <mrow> <msub> <mi>C</mi> <mi>s</mi> </msub> </mrow> </semantics> </math> </inline-formula>) have the most impact on <inline-formula> <math display="inline"> <semantics> <mrow> <msub> <mi>u</mi> <mn>2</mn> </msub> </mrow> </semantics> </math> </inline-formula> and <inline-formula> <math display="inline"> <semantics> <mrow> <msub> <mi>u</mi> <mn>3</mn> </msub> </mrow> </semantics> </math> </inline-formula> responses, respectively. Moreover, the proposed models of the two responses are highly consistent to the experimental results. The proposed regression equations can be applied to solve optimization cost problems.
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