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摘要:
液压泵油膜厚度对润滑性能与工作可靠性具有重要影响，传统数值方法在处理复杂润滑模型时常面临计算效率低、对边界条件依赖性强等问题。为此，提出了一种基于物理信息神经网络(PINN)的液压泵流场建模求解方法，并将其应用于轴向柱塞泵转子-配流盘副的油膜厚度及润滑分析。该方法将雷诺方程、能量方程及混合润滑条件嵌入神经网络的损失函数中，实现物理规律与数据驱动的融合求解。研究结果表明：在典型工况下，PINN 方法能够在无需大量训练数据的情况下，有效求解油膜厚度分布，与数值方法结果吻合较好，相对误差平均值低于 10%，且计算效率显著提高。
Abstract:The oil film thickness in hydraulic pumps significantly impacts their lubrication performance and operational reliability. Traditional numerical methods often face challenges such as low computational efficiency and strong dependence on boundary conditions when handling complex lubrication models. In order to study the oil film thickness and lubrication of the cylinder block/valve plate pair in axial piston pumps, this research suggests a physics-informed neural network (PINN)-based approach for modeling and solving hydraulic pump flow fields. This approach embeds the Reynolds equation, energy equation, and mixed lubrication conditions into the neural network's loss function, achieving a fusion of physical principles and data-driven solutions. Results demonstrate that under typical operating conditions, the PINN method effectively solves oil film thickness distributions without requiring extensive training data. With an average relative error of less than 10%, it shows high agreement with numerical approach findings while greatly increasing computing efficiency.
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图 2 基于PINN的油膜厚度计算流程
Figure 2. Flowchart of PINN-based method for oil film thickness calculation
表 1 PINN与传统神经网络的比较
Table 1. Comparison between PINN and traditional neural networks
网络 目标函数 数据依赖 可解释性 泛化性能 适用场景 传统神经网络 最小化预测误差 需要大量高质量训练数据 黑箱模型，无物理含义 容易过拟合 图像、语音、文本等
数据驱动任务PINN 同时最小化预测误差与
物理方程残差可在稀疏数据条件下训练 内嵌物理约束，具有
物理可解释性泛化能力强 含 PDE 约束的科学计算
与工程建模[24]
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表 2 PINN模型参数
Table 2. Parameters of PINN model
参数 取值 内部采样点数Nf 12000 每个边界采样点数Nb 3000 数据点数量Nd 5000 隐藏层数及神经元 5层，每层128个 激活函数 tanh 学习率 10−3 雷诺方程损失权重 10−4 能量方程损失权重 10−5 压力边界损失权重 10−1 温度边界损失权重 10−2
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表 3 某型航空液压轴向柱塞泵主要参数
Table 3. Main specifications of a specific type of aviation hydraulic axial piston pump
参数 数值 柱塞腔直径/mm 26 斜盘倾角/（°） 15 柱塞长度/mm 150 转速/（r·min−1） 2000 动力黏度/（Pa·s） 0.02 摩擦系数 0.05 弹性模量 2.2×1011 刚度 1×108 油液密度/（kg·m−3） 860
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