Fluid-structure interaction analysis of aviation gear pumps based on conservation-enhanced RBF
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摘要:
针对航空燃油齿轮泵流固耦合模拟中，径向缩放齿轮以连通无间隙齿顶及啮合区流场引起的流固域几何失配问题，以及经典径向基函数（RBF）映射算法忽略物理守恒性导致载荷传递失准风险，在源域与目标域间引入力与力矩守恒约束，采用最小范数法修正目标场网格压力，提出一种守恒性增强的先进RBF数据重构算法，并结合网格分析与试验验证开展某型航空燃油齿轮泵流固耦合仿真。测试算例结果表明先进RBF算法消除了总力和力矩偏差，映射平均误差为
0.0015 %。应用先进守恒RBF加载齿轮泵流场载荷于固体网格节点，静态最大等效应力为31.61 MPa，动态啮合应力峰值为192.18 MPa，流场压力对固体应力和应变的贡献率达到34.38%与29.84%，证明了流固耦合模拟对评估航空燃油齿轮泵实际服役状态的必要性。Abstract:In fluid-structure interaction simulations of aviation gear pumps, two key issues: the distinct geometric mismatch between fluid and solid domains resulting from radially scaling gears to connect gapless tooth tip and meshing zone flow fields; and the notable risk of inaccurate load transfer due to the classical radial basis function (RBF) mapping algorithm neglecting fundamental physical conservation principles, were addressed in this research. To solve these critical problems, force and moment conservation constraints were carefully introduced between the source and target domains. The minimum norm method was effectively employed to correct the target field grid pressure, and an advanced RBF data reconstruction algorithm with significantly enhanced conservation properties was successfully proposed. Combined with detailed grid analysis and rigorous experimental verification, comprehensive fluid-structure interaction simulations were conducted for a specific type of aviation gear pump. Test results showed that the advanced RBF algorithm effectively eliminated total force and moment deviations, with an average mapping error as low as
0.0015 %. When loading flow field loads onto solid grid nodes by the advanced RBF algorithm, the static maximum equivalent stress was measured at 31.61 MPa, and the dynamic meshing stress peak reached 192.18 MPa. The flow field pressure contributed 34.38% to solid stress and 29.84% to strain, respectively. These important findings clearly demonstrate that fluid-structure interaction simulation is highly necessary for accurately evaluating the actual service status of aviation gear pumps in practical operational environments. -
图 3 齿轮泵流固耦合仿真流程
Figure 3. Flowchart of fluid-structure interaction simulation for gear pump
图 17 经典RBF与守恒RBF精度对比
Figure 17. Accuracy comparison between classic RBF and conservative RBF
图 19 施加流体压力载荷的齿轮等效应力云图
Figure 19. Equivalent stress contour map of gears with fluid pressure load applied
表 1 齿轮泵设计参数与工作参数
Table 1. Design and operating parameters of gear pump
参数 数值 设计 模数/mm 2 齿数 13 压力角/（°） 28 中心距/mm 26 齿宽/mm 9.3 工作 进口压力/MPa 0.1 出口压力/MPa 5 转速/（r/min） 8000 工作压力/Pa 101325 工作温度/K 298.15 
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表 2 内流场仿真设置
Table 2. Simulation setup of interior flow field
设置项 具体设置 湍流模型 realizable k-ε 多相流方法 混合模型 动网格方法 2.5D 求解方法 耦合算法 时间步长/10−7 s 7.5 计算步数 10000
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表 3 有限元仿真设置
Table 3. Finite element simulation setup
设置项 具体设置 接触方法 摩擦 摩擦因数 0.1 转速/（r/min） 8000 扭矩/（N·m） 30 时间步长/10−7 s 7.5 计算步数 10000
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表 4 常用全域RBF
Table 4. Commonly used global RBF
全域RBF类型 表达式 Gauss基函数 $\phi （r） ={\mathrm{e}}^{-c^2r^2}$ Inverse quadratic（IQ）
基函数$\phi （r） =\dfrac{1}{ 1+ （ cr ） ^2 }$ Thin-plate spline（TPS）
基函数$\phi （r） =r^2\ln \;r$ Multiquadric（MQ）
基函数$\phi （r） =\sqrt{r^2+c^2}$
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表 5 不同RBF的耗时与映射误差
Table 5. Time consumption and mapping error of different RBF
基函数类型 映射时间/s 平均相对误差/% 最大相对误差/% Gauss 63.054 1.3846 ×10−40.0134 IQ 84.704 8.3313 ×10−40.0055 TPS 35.518 9.8839 ×10−72.3445 ×10−5MQ 64.341 1.9×10−3 0.1602
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表 6 应用经典RBF的流固界面力/力矩数值
Table 6. Numerical calculation of fluid-structure interface force/moment applying classic RBF
物理量 流体域 固体域 总力/N 0.55945 0.61360 总力矩/10−6 （N·m） 8.2302 91.286
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表 7 经典RBF与守恒RBF相对误差比较
Table 7. Comparison of relative errors between classic RBF and conservative RBF
重构方法 最小相对误差 平均相对误差/% 最大相对误差/% 经典RBF 0 0.0007 0.0207 守恒RBF 0 0.0015 0.2193
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表 8 一个啮合周期内最大压力变化趋势
Table 8. Variation trend of the maximum pressure within one meshing cycle
啮合时间 最大压力/MPa 啮合时间 最大压力/MPa $\dfrac{1}{9}T_{\rm{n}}$ 5.31 $\dfrac{6}{9}T_{\rm{n}}$ 5.38 $\dfrac{2}{9}T_{\rm{n}}$ 5.47 $\dfrac{7}{9}T_{\rm{n}}$ 5.48 $\dfrac{3}{9}T_{\rm{n}}$ 5.30 $\dfrac{8}{9}T_{\rm{n}}$ 5.28 $\dfrac{4}{9}T_{\rm{n}}$ 5.48 $T_{\mathrm{n}}$ 5.27 $\dfrac{5}{9}T_{\rm{n}}$ 5.32
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表 9 一个啮合周期内仅施加流体载荷与加入啮合仿真的平均等效应力/应变对比
Table 9. Comparison of average equivalent stress/strain between only applying fluid loads and incorporating meshing simulation within one meshing cycle
强度参数 仅施加流体域
压力载荷流体域压力载荷 +
动态啮合仿真平均等效应力/MPa 1.43 4.16 平均等效应变/10−5 2.05 6.87
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