Abstract
In the present study, a series of dedicated experiments has been performed to observe and measure the build-up of ZDDP tribolayer in rolling/sliding heavily loaded mixed-lubricated contacts. The experiments were carried out using several test configurations. First, ball-on-disc tests were run to investigate the effects of the contact pressure, temperature, and roughness on tribolayer formation. Then, micropitting tests were carried out, with bearing components and with rolling bearings, in order to evaluate the influence of tribolayer build-up on the tribological performance of the rolling/sliding contacts. The obtained experimental data were used first to calibrate a specially developed thermomechanical model and secondly to validate it under different operating conditions and at different levels, up to assessment of the tribological performance, by measuring the level of micropitting on the surfaces. The results show that a relatively simple thermomechanical model can account for tribolayer formation and removal and their effects on the contact performance in a relatively consistent way.
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Abbreviations
- a :
-
Hertzian semi-width in the x-direction (m)
- A :
-
Pre-factor in the modified Arrhenius equation
- C :
-
Pre-factor in the tribolayer growth equation (s−1)
- \(E_{\text{act}}\) :
-
Activation energy for chemical reaction (J)
- g :
-
Coordinate function, \(g = \sqrt {\left( {x - x'} \right)^{2} + \left( {y - y'} \right)^{2} + z^{2} }\) (m)
- h :
-
Local tribolayer thickness (m)
- \(h_{\text{c}}\) :
-
Central lubricant film thickness (m)
- \(h_{\text{f}}\) :
-
Final tribolayer thickness (m)
- \(h_{ \hbox{max} }\) :
-
Local tribolayer thickness limit (m)
- Δh :
-
Net change in the local tribolayer thickness per loading cycle (m)
- \(\Delta h_{\text{TL}}\) :
-
Incremental tribolayer growth per loading cycle (m)
- \(\Delta h_{\text{w}}\) :
-
Local removed material height (due to wear) per load cycle (m)
- H :
-
Hardness of the steel (Pa)
- k :
-
Dimensional Archard’s wear coefficient (s)
- \(k_{\text{B}}\) :
-
Boltzmann constant (J K−1)
- \(k_{\text{s}}\) :
-
Thermal conductivity of steel (W m−1 K−1)
- P :
-
Probability of molecules undergoing a chemical process
- p :
-
Contact pressure (Pa)
- \(p_{\text{o}}\) :
-
Maximum Hertzian contact pressure (Pa)
- q :
-
Heat flux (W m−2)
- q 0 :
-
Amplitude of heat source (W m−2)
- l :
-
Contact length in the rolling direction (x), l ≈ 2a (m)
- R :
-
Fundamental solution associated with heat source shape (J K−1)
- \(R_{\text{q}}\) :
-
R.m.s. for roughness (m)
- S :
-
Slide-to-roll ratio, \(S = (u_{2} - u_{1} )/\bar{u}\)
- \(S_{\text{q}}\) :
-
Area of heat source (m2)
- t :
-
Time (s)
- Δt :
-
Time step in the model (s)
- T :
-
Temperature °C
- u :
-
Surface speed (m s−1)
- U :
-
Mean speed U = (u 2 + u 1)/2 (m s−1)
- \(u_{\text{s}}\) :
-
Sliding speed, \(u_{\text{s}} = (u_{2} - u_{1} )\) (m s−1)
- \(\Delta V_{\text{act}}\) :
-
Activation volume (m3)
- x :
-
Rolling direction coordinate (m)
- x ′ :
-
Rolling direction coordinate of the moving heat flux (m)
- y :
-
Transverse to rolling coordinate (m)
- y ′ :
-
Transverse to rolling coordinate of the moving heat flux (m)
- z :
-
Normal to surface coordinate (m)
- \(\alpha\) :
-
Piezoviscosity coefficient (Pa−1)
- \(\alpha^{\prime}\) :
-
Heat partition function
- \(\eta\) :
-
Dynamic viscosity of the lubricant at the actual temperature (Pa s)
- Λ :
-
Lubrication quality parameter for film thickness Λ = h c /R q
- \(\mu\) :
-
Friction coefficient
- \(\tau\) :
-
Shear stress (Pa)
- \(\tau_{0}\) :
-
Eyring stress of the lubricant (Pa)
- \(\chi\) :
-
Thermal diffusivity of steel (m2 s−1)
- 1, 2 :
-
Corresponds to surface 1 or 2, respectively
- b1, b2 :
-
Corresponds to bulk temperatures
- l :
-
Corresponds to fully lubricated patches of the contact area
- bl :
-
Corresponds to boundary-lubricated patches of the contact area
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Acknowledgements
The authors would like to thank Dr. Stefan Lammens, Director SKF Engineering Research Centre, for his kind permission to publish this article. The research leading to these results has received funding from the People Programme (Marie Curie Actions) of the European Union’s Seventh Framework Programme FP7/2007-2013/ under REA Grant Agreement No. 612603.
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Appendix
Appendix
List of operating conditions, material and lubricant properties in the MTM and MPR tests
Parameters | Description and units | MTM | MPR |
|---|---|---|---|
H | Hardness of the steel, GPa | 6.86 | 6.86 |
\(k_{\text{s}}\) | Thermal conductivity of steel, W m−1 K−1 | 50 | 50 |
\(p_{\text{o}}\) | Maximum Hertzian contact pressure, GPa | 1.28 | 1.5 |
\(R_{\text{q1}}\) | R.m.s. roughness of the ball (MTM) or roller (MPR), nm | 10–15 | 50 |
\(R_{\text{q2}}\) | R.m.s. roughness of the washer (MTM) or rings (MPR), nm | 20–120 | 500 |
S | Slide-to-roll ratio, % | 5 | 2 |
T | Temperature, °C | 40–110 | 40 and 90 |
U | Mean speed, m s−1 | 0.04–0.5 | 0.13 and 1.0 |
\(\alpha\) | Piezoviscosity coefficient, GPa−1 | 10 | 10 |
\(\eta\) | Dynamic viscosity of the lubricant at 40 °C/100 °C, mPa s | 17/3.2 | 343/40 |
Λ | Lubrication quality parameter for film thickness | 0.22–0.27 | 0.34–0.38 |
\(\tau_{0}\) | Eyring stress of the lubricant, MPa | 3 | 3 |
\(\chi\) | Thermal diffusivity of steel, m2 s−1 | 1.34 × 10−5 | 1.34 × 10−5 |
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Brizmer, V., Matta, C., Nedelcu, I. et al. The Influence of Tribolayer Formation on Tribological Performance of Rolling/Sliding Contacts. Tribol Lett 65, 57 (2017). https://doi.org/10.1007/s11249-017-0839-3
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DOI: https://doi.org/10.1007/s11249-017-0839-3