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Finite Element Analysis and Design Research of Composite Transverse Stabilizer Bar
DOI: 10.12677/MOS.2023.126536, PDF, HTML, XML, 下载: 154  浏览: 227

Abstract: Based on the laminated plate theory, combined with the stiffness formula of the isotropic material stabilizer bar and the formula of the equivalent shear modulus of the fiber composite plate, the theoretical formula of the stiffness of the composite stabilizer bar is derived. Then, the stiffness and strength of metal and composite stabilizer bars are analyzed by finite element simulation. In the case of the same stiffness, the strength of the composite stabilizer bar fully meets the requirements, which verifies the reliability of the composite stabilizer bar, and the weight of the composite stabi-lizer bar is reduced by 52.2% compared with the metal stabilizer bar. Finally, the stiffness analysis results are compared with the theoretical calculation, and the error is less than 5%. This study can provide a theoretical reference for the design of this kind of composite stabilizer bar.

1. 引言

2. 稳定杆选材及刚度理论

2.1. 复合材料稳定杆选材

2.2. 金属刚度理论

Figure 1. Stabilizer bar structure dimension parameter diagram

Table 1. Stabilizer rod structure dimensions

(1) BM段的扭转位能。

${U}_{1}=\frac{{F}^{2}\ast \left({L}_{3}+2\ast {L}_{4}\right)}{4GJ}$ (1)

(2) AB段的弯曲位能。

${U}_{2}=\frac{{F}^{2}{L}_{5}^{3}}{6EJ}$ (2)

(3) CK段的弯曲位能。

${U}_{3}={\int }_{0}^{\frac{{L}_{3}}{2}}\frac{{M}^{2}\left(X\right)}{2EJ}\text{d}x=\frac{1}{2EJ}{\int }_{0}^{\frac{{L}_{3}}{2}}{\left[\frac{2F\cdot \left({L}_{4}+{L}_{5}\right)x}{{L}_{3}}\right]}^{2}\text{d}x=\frac{{F}^{2}}{12EJ}{\left({L}_{4}+{L}_{5}\right)}^{2}\cdot {L}_{3}$ (3)

(4) BC段的弯曲位能。

${U}_{4}={\int }_{0}^{{L}_{4}}\frac{{M}^{2}\left(x\right)}{2EJ}\text{d}x=\frac{1}{2EJ}{\int }_{0}^{{L}_{4}}{\left[F\cdot \left({L}_{6}+x\right)\right]}^{2}\text{d}x=\frac{{F}^{2}}{6EJ}\left[{\left({L}_{6}+{L}_{4}\right)}^{2}-{L}_{6}^{2}\right]$ (4)

F所作的功与稳定杆的变形位能相等，则

$\frac{F\cdot f}{2}={U}_{1}+{U}_{2}+{U}_{3}+{U}_{4}$ (5)

$f=\frac{2}{F}\left\{\frac{{F}^{2}\ast \left({L}_{3}+2\ast {L}_{4}\right)}{4GJ}+\frac{{F}^{2}{L}_{5}^{3}}{6EJ}+\frac{{F}^{2}}{12EJ}{\left({L}_{4}+{L}_{5}\right)}^{2}\cdot {L}_{3}+\frac{{F}^{2}}{6EJ}\left[{\left({L}_{6}+{L}_{4}\right)}^{2}-{L}_{6}^{2}\right]\right\}$ (6)

$f=\frac{2}{F}\left\{\frac{{F}^{2}\ast \left({L}_{3}+2\ast {L}_{4}\right)}{4GJ}+\frac{{F}^{2}{L}_{5}^{3}}{6EJ}+\frac{{F}^{2}}{12EJ}{\left({L}_{4}+{L}_{5}\right)}^{2}\cdot {L}_{3}\right\}$

$K=\frac{F}{f}=\frac{1}{\frac{{L}_{3}+2\ast {L}_{4}}{2GJ}+\frac{{L}_{5}^{3}}{3EJ}+\frac{1}{6EJ}{\left({L}_{4}+{L}_{5}\right)}^{2}\cdot {L}_{3}}$ (7)

2.3. 复合材料稳定杆刚度

${E}_{T}={E}_{m}\left(1+{V}_{f}\right)/\left(1-{V}_{f}\right)$ (8)

${E}_{L}={E}_{f}{V}_{f}+{E}_{m}{V}_{m}$ (9)

${G}_{\theta }=\frac{{G}_{12}}{1+\left[\frac{{G}_{12}\left(1+{\mu }_{12}\right)}{{E}_{1}}+\frac{{G}_{12}\left(1+{\mu }_{21}\right)}{{E}_{2}}-1\right]{\mathrm{sin}}^{2}2\theta }$ (10)

${E}_{1}={E}_{L}{V}_{L}+{E}_{T}{V}_{T}$ (11)

$K=\frac{F}{f}=\frac{1}{\frac{{L}_{3}+2\ast {L}_{4}}{2{G}_{\theta }J}+\frac{{L}_{5}^{3}}{3{E}_{1}J}+\frac{1}{6{E}_{1}J}{\left({L}_{4}+{L}_{5}\right)}^{2}\cdot {L}_{3}}$ (12)

$\begin{array}{c}{K}_{45}=\frac{F}{f}=\frac{1}{\frac{{L}_{3}+2\ast {L}_{4}}{2{G}_{45}J}+\frac{{L}_{5}^{3}}{3{E}_{1}J}+\frac{1}{6{E}_{1}J}{\left({L}_{4}+{L}_{5}\right)}^{2}\cdot {L}_{3}}\\ =\frac{1}{\left[\frac{{L}_{3}+2\ast {L}_{4}}{J}\frac{1+{\mu }_{12}}{{E}_{1}}+\frac{{L}_{5}^{3}}{3{E}_{1}J}+\frac{1}{6{E}_{1}J}{\left({L}_{4}+{L}_{5}\right)}^{2}\cdot {L}_{3}\right]}\\ =36.86\text{\hspace{0.17em}}\text{N}/\text{mm}\end{array}$

2.4. 稳定杆关键参数灵敏度分析

(a) (b)

Figure 2. Relationship between stiffness and key parameters: (a) Influence diagram of outside diameter; (b) Influence diagram of elastic modulus

3. 有限元分析

3.1. 有限元模型建立

(a)(b)

Figure 3. Three-dimensional model of stabilizer bar: (a) Metal stabilizer bar model; (b) Composite stabilizer bar model

Table 2. Stabilizer bar mass

3.2. 模型材料设置

Table 3. Glass fiber composite engineering constant

Table 4. Rubber material parameter

3.3. 铺层设计

Figure 4. Composite material apply effect diagram

3.4. 网格划分

3.5. 边界条件与载荷设置

Figure 5. Grid settings

Figure 6. Boundary condition setting

3.6. 稳定杆强度分析

(a)(b)

Figure 8. Stabilizer bar stress cloud diagram. (a) Stress nephogram of metal stabilizer bar; (b) Stress nephogram of composite stabilizer bar

3.7. 稳定杆刚度分析

$K=\frac{F}{L}$ (13)

Figure 9. Stabilizer stiffness calculation model

(a)(b)

Figure 10. Stabilizer rod displacement cloud diagram. (a) Metal stabilizer bar displacement cloud image; (b) Composite stabilizer rod displacement cloud image

Figure 11. Stabilizer bar force-displacement curve

Table 5. Comparison of finite element and theoretical results

3.8. 模态分析

Table 6. Stabilizer rod modal results

4. 结论

NOTES

*通讯作者。

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