Numerical Calculation Method of Multi-Lip Seal Wear under Mixed Thermal Elastohydrodynamic Lubrication
Abstract
:1. Introduction
2. Geometric Structure
3. Theoretical Analysis
3.1. Hydrodynamics
3.2. Contact Mechanics
3.3. Deformation Mechanics
3.4. Thermal Mechanics
3.5. Coupling Mechanics
3.6. Wear Mechanics
3.7. Numerical Calculation Procedure
- In ANSYS software, the finite element analysis (FEA) of seal static solid mechanics is performed based on the characteristics of the seal, fluid and operating conditions.
- The static contact pressure Psc, Lx, K obtained via FEA and the static initial film thickness Hs calculated by Psc are input into the MATLAB program and initialized.
- The film fluid pressure Pf and the asperity contact pressure Pc are calculated using the fluid mechanics model and the contact mechanics model, respectively. Then, compare the sum of Pf and Pc with Psc to obtain the pressure difference under dynamic conditions; the pressure difference is applied to calculate the new film thickness.
- If the film thickness converges, the film temperature can be determined with the thermal mechanics model, which can also determine the fluid viscosity at this temperature convergence via the coupling mechanics model.
- If the fluid viscosity converges, compare whether the fluid flow rate of the three seal lips is equal. If not equal, the pressure in the first and second inter-lip zone is adjusted until the fluid flow rate is balanced.
- If the flow rate is equal, judge whether the stroke is reached. If not, carry on simulating the subsequent time step. The wear mechanics model is used to output the results once all the time steps have been performed.
4. Results and Discussion
4.1. Static Sealing Performance
4.2. Model Validation
4.3. Dynamic Sealing Performance
4.3.1. Effect of Sealed Pressure
4.3.2. Effect of Piston Rod Speed
4.3.3. Effect of Seal Roughness
4.3.4. Effect of Fluid Viscosity
4.3.5. Effect of Ambient Temperature
4.4. Analysis of Seal Wear Characteristics
4.4.1. Effects of Sealed Pressure
4.4.2. Effects of Piston Rod Speed
4.4.3. Effects of Seal Roughness
4.4.4. Effects of Fluid Viscosity
4.4.5. Effects of Ambient Temperature
5. Conclusions
- Some characteristics of the single-lip seal are also reflected in the DAS multi-lip combined seal. The increase in sealed pressure decreases the sealed performance and increases the seal wear rate. When the piston rod speed is increased, the WTR also increases. The high-temperature environment leads to the deterioration of the lubrication characteristics in the sealing zone and increases the seal wear. Therefore, it is not difficult to find that high pressure, high speed and high temperature are still great challenges for the lip seal.
- The load on the sealing zone under mixed lubrication is mainly shared by asperity contact, and the asperity contact load is as high as 50%. When the roughness is greater than 0.6 μm, the seal wear rate clearly increases. Therefore, smaller surface roughness is more conducive in reducing the seal wear and fluid leakage.
- The lubrication characteristics of each seal lip in a DAS multi-lip combined seal largely depend on the working conditions. In the piston rod extension motion, the sealing behavior of each seal lip is not identical due to the existence of critical speed.
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Nomenclature
cc | Specific heat capacity of the cylinder wall |
Dc | Insider diameter of cylinder |
E | Elastic modulus |
F | Cavitation index |
Fn | Normal force |
fc | Friction coefficient for asperity contact |
H | Dimensionless average film thickness, h/σ |
HB | Hardness of the seal material |
Hs | Dimensionless static film thickness, hs/σ |
HT | Dimensionless average truncated film thickness, hT/σ |
∆hw | Seal wear depth |
K | Deformation coefficient matrix |
kc | Thermal conductivity of the cylinder wall |
kn | Seal material wear coefficient, Kn/HB |
L | Contact length of sealing zone |
Lstroke | Cylinder stroke length |
∆L | Relative sliding distance |
Pc | Dimensionless asperity contact pressure, pc/E |
Pf | Dimensionless fluid film pressure, pf/pa |
Pi1, Pi2 | Pressure in the first and second inter-lip region |
Pl | Dimensionless pressure in low-pressure side, pl/pa |
Ps | Dimensionless sealed pressure, ps/pa |
Psc | Dimensionless static contact pressure, psc/E |
pa | Ambient pressure |
pn | Normal contact pressure |
Q | Heat production rate of the cylinder wall, |
Dimensionless flow rate, | |
R | Radius of asperities |
T | Fluid film temperature |
T0 | Ambient temperature |
U | Dimensionless piston rod speed, |
∆Vw | Seal wear volume |
Dimensionless coordinate parallel to the fluid film thickness, x/L | |
z | Dimensionless coordinate normal to the fluid film thickness |
α | Viscosity-pressure coefficient |
Dimensionless pressure-viscosity coefficient, αpa | |
β | Viscosity-temperature coefficient |
ξ | |
Φ | Fluid pressure/density function |
ϕf, ϕfs, ϕfp | Shear stress factors |
ϕs.c.x, ϕxx | Flow factor |
η | Asperity density |
μ0 | Fluid viscosity at atmospheric pressure |
ρc | Density of the cylinder wall |
v | Poisson’s ratio |
ρf | Fluid density |
Dimensionless density, ρ/ρf | |
Dimensionless RMS roughness of the seal, σR1/3η2/3 | |
Dimensionless viscous shear stress, | |
Dimensionless asperity shear stress, |
Abbreviations
DAS | Double-acting seal |
FEA | Finite element analysis |
FEM | Finite element method |
M-EHL | Mixed elastohydrodynamic lubrication |
M-TEHL | Mixed thermal elastohydrodynamic lubrication |
NBR | Nitrile rubber |
PTFE | Polytetrafluoroethylene |
POM | Polyformaldehyde |
RMS | Root mean square |
TPE | Thermoplastic polyester elastomer |
WTR | Wear time rate |
WDR | Wear distance rate |
Appendix A
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Parameter Type | Value |
---|---|
Ambient temperature, T0 | 273.15~313.15 K |
Ambient pressure, p0 | 0.1 MPa |
Fluid viscosity, μ0 | 0.02~0.10 Pa·s |
Viscosity-pressure coefficient, α | 2 × 10−8 Pa−1 |
Viscosity-temperature coefficient, β | 3.17908 × 10−2 K−1 |
Sealed pressure, ps | 2~10 MPa |
Wear coefficient, kn | 1.2 × 10−5 mm3/Nm [31] |
Stroke length, Lstroke | 300 mm |
Insider diameter of cylinder, Dc | 63 mm |
Piston rod extension speed, u | 0.1~0.5 m/s |
Seal RMS roughness, σ | 0.6~1.4 μm |
Friction coefficient, fc | 0.1 [32,33] |
Thermal conductivity of cylinder wall, kc | 46 W/(m·K) |
Density of cylinder wall, ρc | 7850 kg/m3 |
Specific heat capacity of cylinder wall, cc | 460 J/(kg·K) |
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Cheng, D.; Gu, L.; Sun, Y.; Shi, Y. Numerical Calculation Method of Multi-Lip Seal Wear under Mixed Thermal Elastohydrodynamic Lubrication. Lubricants 2023, 11, 248. https://doi.org/10.3390/lubricants11060248
Cheng D, Gu L, Sun Y, Shi Y. Numerical Calculation Method of Multi-Lip Seal Wear under Mixed Thermal Elastohydrodynamic Lubrication. Lubricants. 2023; 11(6):248. https://doi.org/10.3390/lubricants11060248
Chicago/Turabian StyleCheng, Donghong, Lichen Gu, Yu Sun, and Yuan Shi. 2023. "Numerical Calculation Method of Multi-Lip Seal Wear under Mixed Thermal Elastohydrodynamic Lubrication" Lubricants 11, no. 6: 248. https://doi.org/10.3390/lubricants11060248
APA StyleCheng, D., Gu, L., Sun, Y., & Shi, Y. (2023). Numerical Calculation Method of Multi-Lip Seal Wear under Mixed Thermal Elastohydrodynamic Lubrication. Lubricants, 11(6), 248. https://doi.org/10.3390/lubricants11060248