Fractal wear prediction model and numerical analysis of floating ring seal face

doi:10.11949/0438-1157.20221175

Abstract

Abstract:

Aiming at the end face wear of graphite floating ring seal of aero-engine, based on the modified fractal contact theory and Archard wear theory, the fractal wear prediction model of graphite floating ring seal end face is derived from the microscopic point of view, and the test data of literature is used to verify the rationality of the model. Next, numerical simulations were then adopted to analytically study the influence of surface contour parameters and working conditions on the rate of surface wear. The results show that the rate of surface wear first increased before decreasing with fractal dimension, reaching its minimum when the fractal dimension lies between 1.45 and 1.65. Moreover, keeping the fractal dimension constant proves to raise the rate of surface wear with increasing magnitudes of surface feature parameters, friction coefficient and sliding speed of floating ring. The rate of surface wear is mainly related to the smallest level of the frequency component and the seven successive levels of asperities thereafter. By contrast, the influence of the remaining asperities on the overall surface wear rate is negligible.

Key words: fractal, floating ring seal, attrition, contact model, numerical analysis

摘要：

针对航空发动机石墨浮环密封端面磨损问题，基于修正的分形接触理论及Archard磨损理论，从微观角度推导出石墨浮环密封端面的分形磨损预估模型，并采用文献实验数据验证模型的合理性。最后通过数值仿真方法分析研究表面形貌参数及工况参数对浮环密封端面磨损率的影响规律。研究结果表明：石墨浮环密封端面磨损率随着分形维数的增加，先增大后减小，当分形维数处于1.45~1.65时存在最小磨损率；当分形维数一定时，石墨浮环密封端面的磨损率随表面特征尺度、摩擦因数及浮环滑移速度的增大而增大；石墨浮环密封端面的磨损率主要与频率指数最小等级及后续的7个等级微凸体相关，其余微凸体对整个浮环密封端面的磨损率影响可忽略不计。

关键词: 分形, 浮环密封, 磨损, 接触模型, 数值分析

CLC Number:

TH 113.2

Zhimin ZHANG, Xuexing DING, Lanxia ZHANG, Ning LI, Jiaxin SI. Fractal wear prediction model and numerical analysis of floating ring seal face[J]. CIESC Journal, 2022, 73(12): 5526-5536.

张志敏, 丁雪兴, 张兰霞, 力宁, 司佳鑫. 浮环密封端面分形磨损预估模型及数值分析[J]. 化工学报, 2022, 73(12): 5526-5536.

Figures/Tables 13

Fig.1 Schematic diagram of graphite floating ring seal structure

Fig.2 Surface sampling diagram of graphite floating ring

Fig.3 Schematic diagram of floating ring seal end face contact

Fig.4 Schematic diagram of contact between asperity and smooth rigid surface

Table 1 Literature test parameter［29］

模型参数	参数值
钢销弹性模量E₁/ GPa	116.5
摩擦因数f	0.058
特征尺度G/ m	$10 - 9$
钢销屈服应力σ_y/MPa	300
弹性变形磨损系数K_e1	$2 × 10 - 6$
塑性变形磨损系数K_e3	$1 × 10 - 7$
平均滑移速度v/(m/s)	0.69
法向接触载荷P /MPa	0.42
名义接触面积A_a / m²	$4 π × 10 - 6$

Table 1 Literature test parameter［29］

模型参数	参数值
钢销弹性模量E₁/ GPa	116.5
摩擦因数f	0.058
特征尺度G/ m	$10 - 9$
钢销屈服应力σ_y/MPa	300
弹性变形磨损系数K_e1	$2 × 10 - 6$
塑性变形磨损系数K_e3	$1 × 10 - 7$
平均滑移速度v/(m/s)	0.69
法向接触载荷P /MPa	0.42
名义接触面积A_a / m²	$4 π × 10 - 6$

Fig.5 Comparison between experimental data in literature and this model

Table 2 Floating ring shape parameters， material parameters and working condition parameters［14，30］

模型参数	参数值
合金钢弹性模量E₂/ GPa	365
石墨弹性模量E₃/ GPa	20
石墨屈服应力σ_y/ MPa	50
合金钢泊松比ν₁	0.24
石墨泊松比ν₂	0.29
弹性变形磨损系数K_e1	$2 × 10 - 7$
弹塑性变形磨损系数K_e2	$1 × 10 - 7$
塑性变形磨损系数 K_e3	$1 × 10 - 8$
平均滑移速度 v/(m/s)	0.176×10^-3
石墨浮环密封端面内径d₁/m	0.0832
石墨浮环密封端面外径d₂ $/ m$	0.0898
石墨浮环端面载荷P /MPa	0.28

Table 2 Floating ring shape parameters， material parameters and working condition parameters［14，30］

模型参数	参数值
合金钢弹性模量E₂/ GPa	365
石墨弹性模量E₃/ GPa	20
石墨屈服应力σ_y/ MPa	50
合金钢泊松比ν₁	0.24
石墨泊松比ν₂	0.29
弹性变形磨损系数K_e1	$2 × 10 - 7$
弹塑性变形磨损系数K_e2	$1 × 10 - 7$
塑性变形磨损系数 K_e3	$1 × 10 - 8$
平均滑移速度 v/(m/s)	0.176×10^-3
石墨浮环密封端面内径d₁/m	0.0832
石墨浮环密封端面外径d₂ $/ m$	0.0898
石墨浮环端面载荷P /MPa	0.28

Fig.6 Relationship of D-h-G

Fig.7 The diagram of optimal fractal dimension

Fig.8 Relationship of friction coefficient and wear rate

Table 3 The critical frequency index of asperities

D	G/m	n_ec	n_epc	n_pc
1.5	$1 × 10 - 9$	20	25	32
1.6	$1 × 10 - 9$	25	29	35
1.7	$1 × 10 - 9$	29	32	37

Table 3 The critical frequency index of asperities

D	G/m	n_ec	n_epc	n_pc
1.5	$1 × 10 - 9$	20	25	32
1.6	$1 × 10 - 9$	25	29	35
1.7	$1 × 10 - 9$	29	32	37

Fig.9 Relationship of frequency index and wear rate

Fig.10 Relationship of slip velocity and wear rate

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