Tribodynamic modeling of piston compression ring and cylinder liner conjunction in high-pressure zone of engine cycle

Abstract

Piston compression ring and cylinder liner contact contributes a significant part of friction loss in an engine. Most of this loss occurs during compression and power stroke transition (i.e., between 300° to 400° crank position). It is because of the combustion gas pressure is higher in this region to enhance ring–liner contact friction. In this paper, we developed a tribodynamic model to study the transient thermoelastohydrodynamics of ring–liner contact. It takes into account the combined solution of Reynolds equation, energy equation, and elastic deformation equation considering ring–liner conformability and rheology change. We estimate the minimum film profile, friction force, and friction power loss within a high-pressure zone of a high-performance engine. Roughness of the liner is characterized using R _k parameter for better surface representation.

Appendix

The flow factors in any location are 3-D parameters. They are based on the Stribeck’s oil film parameter. The following flow factors are used in Reynolds Eq. (9):

$$ {\text{Pressure flow factor}}:{\phi_{\text{p}}} = \left\{ {\matrix{ {1 - {C_{{{\phi_x}}}}{e^{{ - {r_{{{\phi_x}}}}{\lambda_{\text{rk}}}}}}} \hfill &{{\text{for}}\;{\gamma_{\text{c}}} \leqslant 1} \hfill \\ {1 + {C_{{{\phi_x}}}}{e^{{ - {r_{{{\phi_x}}}}{\lambda_{\text{rk}}}}}}} \hfill &{{\text{for}}\;{\gamma_{\text{c}}} > 1} \hfill \\ }<!end array> } \right\} $$

(21)

$$ {\text{Shear flow factor}}:{\phi_{\text{s}}} = \left\{ {\matrix{ {{A_{{1\left( {{\phi_{\text{s}}}} \right)}}}{\lambda_{\text{rk}}}^{{{\alpha_{{1\left( {{\phi_{\text{s}}}} \right)}}}}}{e^{{ - {\alpha_{{2\left( {{\phi_{\text{s}}}} \right)}}}\lambda + {\alpha_{{3\left( {{\phi_{\text{s}}}} \right)}}}{\lambda^2}}}}} \hfill &{{\lambda_{\text{rk}}} \leqslant 5} \hfill \\ {{A_{{2\left( {{\phi_{\text{s}}}} \right)}}}{e^{{ - 0.25{\lambda_{\text{rk}}}}}}} \hfill &{{\lambda_{\text{rk}}} > 5} \hfill \\ }<!end array> } \right\} $$

(22)

$$ {\text{Geometric flow factor}}:{\phi_{\text{g}}} = \frac{1}{{6\sqrt {{{\lambda_{\text{rk}}}}} }} + \frac{1}{2} + \frac{{{\lambda_{\text{rk}}}}}{{2\sqrt {6} }} + \frac{{{\lambda_{\text{rk}}}^2}}{{36}} $$

(23)

The following flow factors are used in the shear stress Eq. (10):

Pressure-induced flow factor: ${\phi_{\text{fp}}} = 1 - {D_{{\left( {{\phi_{\text{fp}}}} \right)}}}{e^{{ - {s_{{\left( {{\phi_{\text{fp}}}} \right)}}}{\lambda_{\text{rk}}}}}}$

Shear-induced flow factor:

${\phi_{\text{fs}}} = \left\{ {\matrix{ {{A_{{3\left( {{\phi_{\text{fs}}}} \right)}}}{\lambda_{{rk}}}^{{{\alpha_{{4\left( {{\phi_{\text{fs}}}} \right)}}}}}{e^{{ - {\alpha_{{5\left( {{\phi_{{_{\text{fs}}}}}} \right)}}}{\lambda_{{rk}}} + {\alpha_{{6\left( {{\phi_{\text{fs}}}} \right)}}}{\lambda_{\text{rk}}}^2}}}} \hfill &{{\text{for}}\;0.5 < {\lambda_{\text{rk}}} < 7.0} \hfill \\ 0 \hfill &{{\text{for}}\;{\lambda_{\text{rk}}} > 7.0} \hfill \\ }<!end array> } \right\}$

And for topographical flow factor, the following holds:for ${\lambda_{\text{rk}}} \leqslant 3,{\phi_{\text{fg}}} = \frac{{35}}{{32}}\varsigma \left\{ {{{\left( {1 - \varsigma } \right)}^3}\ln \frac{{\varsigma + 1}}{{{ \in^{*}}}} + \frac{1}{{60}}\left[ { - 55 + \varsigma \left( {\varsigma \left( {132 + \varsigma \left( {345 + \varsigma \left( { - 160 + \varsigma \left( { - 405 + \varsigma \left( {60 + 147\varsigma } \right)} \right)} \right)} \right)} \right)} \right)} \right]} \right\}$ and for ${\lambda_{\text{rk}}} > 3$,

$$ {\phi_{\text{fg}}} = \frac{{35}}{{32}}\varsigma \left\{ {{{\left( {1 - {\varsigma^2}} \right)}^3}\ln \frac{{\varsigma + 1}}{{\varsigma - 1}} + \frac{\varsigma }{{15}}\left[ {66 + {\varsigma^2}\left( {30{\varsigma^2} - 80} \right)} \right]} \right\} $$

where ${\lambda_{\text{rk}}} = \frac{h}{{{R_{\text{k}}}}},\varsigma = \frac{{{\lambda_{\text{rk}}}}}{3},{ \in^{*}} = \frac{ \in }{{3{R_{\text{k}}}}},{\text{and}}\; \in = \frac{{{R_{\text{k}}}}}{{100}}.$

All the constants used in the above flow factors are taken from Patir and Cheng [13] for an isotropic surface.