气体润滑机械密封端面型槽的拓扑优化

doi:10.11949/0438-1157.20251475

摘要/Abstract

摘要：

针对参数化优化方法在机械密封端面槽型优化上的局限性，以涡轮泵用深冷低粘气氧润滑机械密封端面为优化对象，提出了一种适用于气体润滑密封型槽设计的拓扑优化方法并构建相应的拓扑优化模型，基于有限元方法开展了多工况和几何参数下的槽型拓扑优化设计。研究表明，该方法具有较好的鲁棒性且对初始拓扑结构不敏感，获得的型槽拓扑结构与基于反应扩散方程的拓扑优化方法获得的液体润滑端面型槽结构相似。最终优化槽型与槽坝比、槽深比、设计域周向角以及密封压力、转速相关，推荐的槽坝比为0.7-0.8，槽深比为3.0-3.5。在相同周向角和槽深比条件下，拓扑优化型槽相较于传统螺旋槽展现出更优的综合密封性能：气膜开启力平均提升3.78%–5.64%，泄漏率平均降低3.95%–10.22%。为高性能气体润滑端面密封设计提供了可靠的理论依据与参数指导。

关键词: 设计优化, 气体, 数值模拟, 拓扑优化, 机械密封

Abstract:

To address the limitations of parametric optimization methods in groove profile design for mechanical seal faces, the end face of a cryogenic low-viscosity oxygen‑lubricated mechanical seal for turbopumps was taken as the optimization target. A topology optimization methodology applicable to the design of grooves in gas-lubricated seals was proposed, and a corresponding topology optimization model was established. Based on the finite element method, topology optimization of groove profiles was conducted under multiple operating conditions and geometric parameters. Results demonstrate good robustness and insensitivity to the initial topology, with the obtained groove topology resembling that derived from reaction‑diffusion equation‑based topology optimization for liquid‑lubricated seal faces. The optimized groove profile depends on the groove‑land ratio, groove‑depth ratio, circumferential angle of the design domain, sealing pressure, and rotational speed, with recommended values of 0.7–0.8 and 3.0–3.5 for groove‑land and groove‑depth ratios, respectively. Under identical circumferential angle and groove‑depth ratio conditions, the topology‑optimized groove outperforms conventional spiral grooves in overall sealing performance: the average gas film opening force increases by 3.78%–5.64%, while the leakage rate decreases by 3.95%–10.22%. A reliable theoretical basis and parameter guidance is provided for the design of high-performance gas-lubricated face seals.

Key words: optimal design, gas, numerical simulation, topology optimization, mechanical seals

章凯, 冯晓东, 孟祥铠, 江锦波, 赵文静, 彭旭东. 气体润滑机械密封端面型槽的拓扑优化[J]. 化工学报, DOI: 10.11949/0438-1157.20251475.

Kai ZHANG, Xiaodong FENG, Xiangkai MENG, Jinbo JIANG, Wenjing ZHAO, Xudong PENG. End face groove topology optimization of for gas-lubricated mechanical seals[J]. CIESC Journal, DOI: 10.11949/0438-1157.20251475.

图/表 18

图1 几何模型注:(a) 几何模型 (b)计算区域

Fig.1 Geometrical model

图2 数值计算流程

Fig.2 Numerical procedure

图3 优化方法验证

Fig.3 Optimization method validation

表1 型槽计算参数

Table 1 Calculation parameters of grooves

参数	数值	参数	数值
外径半径r_o/mm	55	外径压力p_s/MPa	3.0
内径半径r_i/mm	45	内径压力p_a/MPa	0.1
气膜膜厚h_o/μm	2.0	转速n/(r $/$ min)	30 000
槽深h_g/μm	6.0	动力粘度μ/(Pa $∙$ s)	1.25×10^-5
槽坝比ζ	0.7	温度T/K	160
周向角α/rad	π/6	气体常数R/(J $·$ (kg $∙$ T)^-1)	260

表1 型槽计算参数

Table 1 Calculation parameters of grooves

参数	数值	参数	数值
外径半径r_o/mm	55	外径压力p_s/MPa	3.0
内径半径r_i/mm	45	内径压力p_a/MPa	0.1
气膜膜厚h_o/μm	2.0	转速n/(r $/$ min)	30 000
槽深h_g/μm	6.0	动力粘度μ/(Pa $∙$ s)	1.25×10^-5
槽坝比ζ	0.7	温度T/K	160
周向角α/rad	π/6	气体常数R/(J $·$ (kg $∙$ T)^-1)	260

图4 网格数的影响

Fig.4 Influence of mesh number

图5 扩散系数的影响

Fig.5 Effect of the diffusion coefficient

图6 不同初始拓扑的优化过程

Fig.6 Optimization process with different initial topologies

图7 初始拓扑结构的影响

Fig.7 Effect of the initial topology

图8 槽坝比的影响

Fig.8 Effect of the groove-to-ridge ratio

图9 不同槽坝比下密封端面的膜压分布

Fig.9 Film Pressure distribution of the seal groove profile under different dam-groove ratios

图10 周向角的影响

Fig.10 Effect of the circumferential angles

图11 槽深比的影响

Fig. 11 Effect of the groove depth ratio

图12 密封压力的影响

Fig. 12 Effect of the sealing pressure

图13 转速的影响

Fig. 13 Effect of the rotational speed

图14 变工况条件下的端面压力分布云图

Fig.14 Pressure distribution contours on the sealing face under varying operating conditions

表2 组合参数型槽优化参数

Table 2 Optimization parameters for the groove with combined parameters

参数编号	槽坝比ζ	槽深比ξ	周向角α/rad	开启力F_open/N	气膜刚度K/(N $/$ m)	泄漏率Q/(g $/$ s)	摩擦功耗W_f/W
1	0.7	2.0	π/6	9 563.64	2.16×10⁹	0.668	404.48
2	0.7	2.0	2π/15	9 638.54	2.07×10⁹	0.695	399.85
3	0.7	2.0	π/9	9 665.93	2.01×10⁹	0.714	397.31
4	0.7	2.5	π/6	9 813.09	2.07×10⁹	0.722	395.95
5	0.7	2.5	2π/15	9 831.36	1.93×10⁹	0.735	393.77
6	0.7	2.5	π/9	9 829.04	1.84×10⁹	0.748	392.29
7	0.7	3.0	π/6	9 908.90	1.86×10⁹	0.741	389.92
8	0.7	3.0	2π/15	9 884.49	1.70×10⁹	0.746	388.52
9	0.7	3.0	π/9	9 858.46	1.59×10⁹	0.752	387.73
10	0.7	3.5	π/6	9 913.79	1.63×10⁹	0.742	384.69
11	0.7	3.5	2π/15	9 852.57	1.46×10⁹	0.738	383.83
12	0.7	3.5	π/9	9 807.01	1.33×10⁹	0.740	383.46
13	0.8	2.0	π/6	9 630.18	2.19×10⁹	0.753	399.81
14	0.8	2.0	2π/15	9 691.87	2.09×10⁹	0.793	394.24
15	0.8	2.0	π/9	9 715.03	2.02×10⁹	0.822	391.09
16	0.8	2.5	π/6	9 892.54	2.07×10⁹	0.838	389.44
17	0.8	2.5	2π/15	9 905.99	1.93×10⁹	0.868	385.60
18	0.8	2.5	π/9	9 901.31	1.85×10⁹	0.893	383.49
19	0.8	3.0	π/6	10 002.60	1.85×10⁹	0.881	381.17
20	0.8	3.0	2π/15	9 974.56	1.70×10⁹	0.899	378.60
21	0.8	3.0	π/9	9 954.29	1.60×10⁹	0.918	376.69
22	0.8	3.5	π/6	10 024.40	1.62×10⁹	0.900	373.51
23	0.8	3.5	2π/15	9 962.18	1.45×10⁹	0.906	372.22
24	0.8	3.5	π/9	9 922.17	1.35×10⁹	0.916	371.14

表2 组合参数型槽优化参数

Table 2 Optimization parameters for the groove with combined parameters

参数编号	槽坝比ζ	槽深比ξ	周向角α/rad	开启力F_open/N	气膜刚度K/(N $/$ m)	泄漏率Q/(g $/$ s)	摩擦功耗W_f/W
1	0.7	2.0	π/6	9 563.64	2.16×10⁹	0.668	404.48
2	0.7	2.0	2π/15	9 638.54	2.07×10⁹	0.695	399.85
3	0.7	2.0	π/9	9 665.93	2.01×10⁹	0.714	397.31
4	0.7	2.5	π/6	9 813.09	2.07×10⁹	0.722	395.95
5	0.7	2.5	2π/15	9 831.36	1.93×10⁹	0.735	393.77
6	0.7	2.5	π/9	9 829.04	1.84×10⁹	0.748	392.29
7	0.7	3.0	π/6	9 908.90	1.86×10⁹	0.741	389.92
8	0.7	3.0	2π/15	9 884.49	1.70×10⁹	0.746	388.52
9	0.7	3.0	π/9	9 858.46	1.59×10⁹	0.752	387.73
10	0.7	3.5	π/6	9 913.79	1.63×10⁹	0.742	384.69
11	0.7	3.5	2π/15	9 852.57	1.46×10⁹	0.738	383.83
12	0.7	3.5	π/9	9 807.01	1.33×10⁹	0.740	383.46
13	0.8	2.0	π/6	9 630.18	2.19×10⁹	0.753	399.81
14	0.8	2.0	2π/15	9 691.87	2.09×10⁹	0.793	394.24
15	0.8	2.0	π/9	9 715.03	2.02×10⁹	0.822	391.09
16	0.8	2.5	π/6	9 892.54	2.07×10⁹	0.838	389.44
17	0.8	2.5	2π/15	9 905.99	1.93×10⁹	0.868	385.60
18	0.8	2.5	π/9	9 901.31	1.85×10⁹	0.893	383.49
19	0.8	3.0	π/6	10 002.60	1.85×10⁹	0.881	381.17
20	0.8	3.0	2π/15	9 974.56	1.70×10⁹	0.899	378.60
21	0.8	3.0	π/9	9 954.29	1.60×10⁹	0.918	376.69
22	0.8	3.5	π/6	10 024.40	1.62×10⁹	0.900	373.51
23	0.8	3.5	2π/15	9 962.18	1.45×10⁹	0.906	372.22
24	0.8	3.5	π/9	9 922.17	1.35×10⁹	0.916	371.14

图15 螺旋槽机械密封端面

Fig.15 Spiral groove mechanical seal face

图16 拓扑优化槽与螺旋槽对比

Fig.16 Topological vs. spiral groove comparison

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