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Influence Law of Sun Wheel Bearing Support Stiffness on the Uniform Load Characteristics of Planetary Gear Transmission System
DOI: 10.12677/MET.2022.113023, PDF, HTML, XML, 下载: 49  浏览: 93  科研立项经费支持

Abstract: In this paper, the dynamics model of a single-row 2K-H planetary gear reducer is established, and its vibration differential equations are derived. Using the parameters of an experimental gearbox as simulation parameters, a simulation study was conducted on the influence law of support stiffness on the equal load characteristics of the planetary gear transmission system. It is found that the use of a smaller support stiffness of the sun wheel bearing can optimize the equal load characteristics of the internal meshing pair of the system, and a smaller support stiffness means that the center member has a certain floating effect, which can optimize the equal load characteristics.

1. 引言

1.1. 行星齿轮机构的力学模型

Figure 1. Sketch of the transmission of planetary gear system

Figure 2. Dynamics model of planetary gearing system

Table 1. Main parameters of the system

1.2. 试验用单排行星齿轮机构的运动微分方程

Table 2. Main error parameters of the system

$\left\{\begin{array}{l}{e}_{s2pi}\left(t\right)={e}_{{a}_{s2pi}}\mathrm{sin}\left(\omega t+{\beta }_{s2i}\right)+{F}_{s2}\mathrm{sin}\left[{\omega }_{s2c}t+{\beta }_{s2}-\frac{2\pi \left(i-1\right)}{N}+\alpha \right]+{F}_{p2i}\mathrm{sin}\left({\omega }_{p2c}t+{\beta }_{p2i}+\alpha \right)\\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}+{A}_{s2}\mathrm{sin}\left(-{\omega }_{c2}t+{\gamma }_{s2}+\alpha -\frac{2\pi \left(i-1\right)}{N}\right)+{A}_{p2i}\mathrm{sin}\left({\gamma }_{p2i}+\alpha \right)\\ {e}_{r2pi}\left(t\right)={e}_{{a}_{r2pi}}\mathrm{sin}\left(\omega t+{\beta }_{r2i}\right)+{F}_{p2i}\mathrm{sin}\left({\omega }_{p2c}t+{\beta }_{p2i}+\alpha \right)\\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}-{F}_{r2}\mathrm{sin}\left[{\omega }_{r2c}t+{\beta }_{r2}-\frac{2\pi \left(i-1\right)}{N}+\alpha \right]+{A}_{p2i}\mathrm{sin}\left({\gamma }_{p2i}-\alpha \right)\end{array}$ (1)

${x}_{s2di}=-{\xi }_{s2}\mathrm{sin}\left({\phi }_{i}-\alpha \right)+{\eta }_{s2}\mathrm{cos}\left({\phi }_{i}-\alpha \right)$ (2)

${F}_{s2p2i}={k}_{s2p2i}f\left({x}_{s2p2i}+{x}_{s2di}-{e}_{s2p2i},{b}_{s2p2i}\right)$ (3)

${F}_{r2p2i}={k}_{r2p2i}f\left({x}_{r2p2i}-{e}_{r2p2i},{b}_{r2p2i}\right)$ (4)

${F}_{s2p2i,d}$${F}_{r2p2i,d}$ 分别表示太阳轮和内齿轮与第i个行星轮之间的啮合阻尼力，则

${F}_{s2p2i,d}={c}_{s2p2i}\left({\stackrel{˙}{x}}_{s2p2i}+{\stackrel{˙}{x}}_{s2di}-{\stackrel{˙}{e}}_{s2p2i}\right)$ (5)

${F}_{r2p2i,d}={c}_{r2p2i}\left({\stackrel{˙}{x}}_{r2p2i}-{\stackrel{˙}{e}}_{r2p2i}\right)$ (6)

$\begin{array}{l}{m}_{h,eq}{\stackrel{¨}{x}}_{h}+{c}_{hs2,eq}{x}_{hs2}+{k}_{hs2,eq}{x}_{hs2}={F}_{h}\\ {m}_{s2,eq}{\stackrel{¨}{x}}_{s2}-{c}_{hs2,eq}{\stackrel{˙}{x}}_{hs2}+\underset{i=1}{\overset{4}{\sum }}{F}_{s2p2i}^{d}-{k}_{hs2,eq}{x}_{hs2}+\underset{i=1}{\overset{4}{\sum }}{F}_{s2p2i}=0\\ {m}_{s2}{\stackrel{¨}{\xi }}_{s2}+c{2}_{\xi }{\stackrel{˙}{\xi }}_{s2}-\underset{i=1}{\overset{4}{\sum }}{F}_{s2p2i}^{d}\mathrm{sin}\left({\phi }_{i}-\alpha \right)+k{2}_{\xi }{\xi }_{s2}-\underset{i=1}{\overset{4}{\sum }}{F}_{s2p2i}\mathrm{sin}\left({\phi }_{i}-\alpha \right)=0\\ {m}_{s2}{\stackrel{¨}{\eta }}_{s2}+c{2}_{\eta }\stackrel{˙}{\eta }{2}_{s2}+\underset{i=1}{\overset{4}{\sum }}{F}_{s2p2i}^{d}\mathrm{cos}\left({\phi }_{i}-\alpha \right)+k{2}_{\eta }{\eta }_{s2}+\underset{i=1}{\overset{4}{\sum }}{F}_{s2p2i}\mathrm{cos}\left({\phi }_{i}-\alpha \right)=0\\ {m}_{pi,eq}{\stackrel{¨}{x}}_{p2i}-{F}_{s2p2i}^{d}+{F}_{r2p2i}^{d}-{F}_{s2p2i}+{F}_{r2p2i}=0\end{array}$

$\begin{array}{l}{m}_{c,eq}{\stackrel{¨}{x}}_{c}-\underset{i=1}{\overset{4}{\sum }}{F}_{s2p2i}^{d}-\underset{i=1}{\overset{4}{\sum }}{F}_{r2p2i}^{d}+{c}_{cl,eq}{\stackrel{˙}{x}}_{cl}-\underset{i=1}{\overset{4}{\sum }}{F}_{s2p2i}-\underset{i=1}{\overset{4}{\sum }}{F}_{r2p2i}+{k}_{cl,eq}{x}_{cl}=0\\ {m}_{l,eq}{\stackrel{¨}{x}}_{l}-{c}_{cl,eq}{\stackrel{˙}{x}}_{cl}-{k}_{cl,eq}{x}_{l}=-{F}_{l}\\ {m}_{c2,eq}=\frac{{I}_{c2}}{{r}_{bc2}^{2}}+3\frac{{m}_{p2}}{{\mathrm{cos}}^{2}\alpha }\\ {m}_{h,eq}=\frac{{I}_{h}}{{r}_{bs2}^{2}}\begin{array}{cc}& \end{array}{m}_{s2,eq}=\frac{{I}_{s2}}{{r}_{bs2}^{2}}\\ {m}_{l,eq}=\frac{{I}_{h}}{{r}_{bc}^{2}}\begin{array}{cc}& \end{array}{m}_{pi,eq}=\frac{{I}_{pi}}{{r}_{bp}^{2}}\end{array}$

$\begin{array}{l}{k}_{hs2,eq}=\frac{{k}_{bs2}}{{r}_{bs2}^{2}}\begin{array}{cc}& \end{array}{k}_{cl,eq}=\frac{{k}_{cl}}{{r}_{bc}^{2}}\\ {c}_{hs2.eq}=\frac{{c}_{hs2}}{{r}_{bs2}^{2}}\begin{array}{cc}& \end{array}{c}_{cl,eq}=\frac{{c}_{cl}}{{r}_{bc}^{2}}\\ F=\frac{{T}_{h}}{{r}_{bs}}\begin{array}{cc}& \end{array}{F}_{1}=\frac{{T}_{1}}{{r}_{bc}}\\ i=1,2,3\end{array}$ (7)

2. 单排行星机构均载特性的计算与分析

Figure 3. Riation of the mean load coefficient when the bearing support stiffness is 3 × 106 N/m

Figure 4. Bearing support stiffness of 3 × 106 N/m external meshing vice dynamic load variation

Figure 5. Variation of dynamic load on the internal meshing pair when the bearing support stiffness is 3 × 106 N/m

Figure 6. Variation of the mean load coefficient when the bearing support stiffness is 3 × 107 N/m

Figure 7. Variation of dynamic load on the outer meshing pair when the bearing support stiffness is 3 × 107 N/m

Figure 8. Variation of dynamic load on the internal meshing pair when the bearing support stiffness is 3 × 107 N/m

Figure 9. Variation of the average load factor when the bearing support stiffness is 3 × 108 N/m

Figure 10. Variation of dynamic load of outer meshing vice when bearing support stiffness is 3 × 108 N/m

3. 结论

Figure 11. Variation of dynamic load on the internal meshing pair when the bearing support stiffness is 3 × 108 N/m

NOTES

*通讯作者。

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