Effects of Vibration Isolator on Compound Planetary Gear Train with Marine Twin-Layer Gearbox Case: a Dynamic Load Analysis

Abstract

Purpose

This study aims to take the compound planetary gear train as an example to investigate how the vibration isolator affects the dynamic characteristics of the gear system.

Methods

The dynamic parameters are obtained from the finite element model of the gearbox case with the vibration isolators by the substructure method. The lumped mass method is used to construct the systematic coupled dynamic model of the compound planetary gear train with the marine twin-layer gearbox case. The dynamic response of the coupled system is calculated by the numerical calculation method of the Fourier series.

Results

The number of vibration isolators negatively affects the bearing forces of the input shaft, output shaft, and planets. The influence of the number of vibration isolators on LSCs is different in the differential stage and the encased stage. When the vibration isolators stiffness is less than 200 N/μm, the stiffness of the vibration isolator has a significant effect on the bearing forces of the input shaft, output shaft, and planets. The increase in the stiffness of the vibration isolator would increase the LSCs of the differential stage and decrease the LSCs of the encased stage.

Conclusions

The number and stiffness of the vibration isolator have influences on the bearing forces and the LSCs. Compared with the LSCs in the differential stage, the LSCs in the encased stage are more sensitive to the number and stiffness of vibration isolators.

Appendix

$$ \varvec{K}_{pi}^{b} = \left[ {\begin{array}{*{20}c} 0 & 0 & 0 \\ 0 & {k_{xx}^{p} } & {k_{xy}^{p} } \\ 0 & {k_{yx}^{p} } & {k_{yy}^{p} } \\ \end{array} } \right],\;\varvec{C}_{pi}^{b} = \left[ {\begin{array}{*{20}c} 0 & 0 & 0 \\ 0 & {c_{xx}^{p} } & {c_{xy}^{p} } \\ 0 & {c_{yx}^{p} } & {c_{yy}^{p} } \\ \end{array} } \right], $$

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$$ \left\{ {\begin{array}{*{20}c} {\varvec{F}_{pi}^{b} = \left[ {\begin{array}{*{20}c} 0 & {F_{Hcpi} } & {F_{Vcpi} } \\ \end{array} } \right]^{\text{T}} } \\ {\varvec{X}_{c} = \left[ {\begin{array}{*{20}c} {x_{c} } & {H_{c} } & {V_{c} } \\ \end{array} } \right]^{\text{T}} } \\ {\varvec{X}_{pi} = \left[ {\begin{array}{*{20}c} {x_{pi} } & {H_{pi} } & {V_{pi} } \\ \end{array} } \right]^{\text{T}} } \\ \end{array} } \right., $$

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$$ \varvec{K}_{\text{in}}^{b} = \left[ {\begin{array}{*{20}c} 0 & 0 & 0 \\ 0 & {k_{xx}^{\text{in}} } & {k_{xy}^{\text{in}} } \\ 0 & {k_{yx}^{\text{in}} } & {k_{yy}^{\text{in}} } \\ \end{array} } \right],\varvec{C}_{\text{in}}^{b} = \left[ {\begin{array}{*{20}c} 0 & 0 & 0 \\ 0 & {c_{xx}^{\text{in}} } & {c_{xy}^{\text{in}} } \\ 0 & {c_{yx}^{\text{in}} } & {c_{yy}^{\text{in}} } \\ \end{array} } \right], $$

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$$ \varvec{K}_{\text{out}}^{b} = \left[ {\begin{array}{*{20}c} 0 & 0 & 0 \\ 0 & {k_{xx}^{\text{out}} } & {k_{xy}^{\text{out}} } \\ 0 & {k_{yx}^{\text{out}} } & {k_{yy}^{\text{out}} } \\ \end{array} } \right],\;\varvec{C}_{\text{in}}^{b} = \left[ {\begin{array}{*{20}c} 0 & 0 & 0 \\ 0 & {c_{xx}^{\text{out}} } & {c_{xy}^{\text{out}} } \\ 0 & {c_{yx}^{\text{out}} } & {c_{yy}^{\text{out}} } \\ \end{array} } \right], $$

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$$ \left\{ {\begin{array}{*{20}c} {\varvec{F}_{\text{in}}^{b} = \left[ {\begin{array}{*{20}c} 0 & {F_{H}^{\text{in}} } & {F_{V}^{\text{in}} } \\ \end{array} } \right]^{\text{T}} } \\ {\varvec{X}_{\text{in}}^{g} = \left[ {\begin{array}{*{20}c} 0 & {H_{\text{in}}^{g} } & {V_{\text{in}}^{g} } \\ \end{array} } \right]^{\text{T}} } \\ {\varvec{F}_{\text{out}}^{b} = \left[ {\begin{array}{*{20}c} 0 & {F_{H}^{\text{out}} } & {F_{V}^{\text{out}} } \\ \end{array} } \right]^{\text{T}} } \\ {\varvec{X}_{\text{out}}^{g} = \left[ {\begin{array}{*{20}c} 0 & {H_{\text{out}}^{g} } & {V_{\text{out}}^{g} } \\ \end{array} } \right]^{\text{T}} } \\ \end{array} } \right., $$

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$$ \varvec{K}_{mj}^{b} = \left[ {\begin{array}{*{20}c} 0 & 0 & 0 \\ 0 & {k_{xx}^{m} } & {k_{xy}^{m} } \\ 0 & {k_{yx}^{m} } & {k_{yy}^{m} } \\ \end{array} } \right],\;\varvec{C}_{mj}^{b} = \left[ {\begin{array}{*{20}c} 0 & 0 & 0 \\ 0 & {c_{xx}^{m} } & {c_{xy}^{m} } \\ 0 & {c_{yx}^{m} } & {c_{yy}^{m} } \\ \end{array} } \right], $$

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$$ \left\{ {\begin{array}{*{20}c} {\varvec{F}_{mj}^{b} = \left[ {\begin{array}{*{20}c} 0 & {F_{Hbmj} } & {F_{Vbmj} } \\ \end{array} } \right]^{\text{T}} } \\ {\varvec{X}_{mj}^{g} = \left[ {\begin{array}{*{20}c} 0 & {H_{b}^{j} } & {V_{b}^{j} } \\ \end{array} } \right]^{\text{T}} } \\ {\varvec{X}_{mj} = \left[ {\begin{array}{*{20}c} {x_{mj} } & {H_{mj} } & {V_{mj} } \\ \end{array} } \right]^{\text{T}} } \\ \end{array} } \right.. $$

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