Inflation pressure effect on whole tyre hysteresis ratio and radial spring constant

Abstract

<smarttagtype namespaceuri="urn:schemas-microsoft-com:office:smarttags" name="City"><smarttagtype namespaceuri="urn:schemas-microsoft-com:office:smarttags" name="place"> The basic equation for rolling loss <i style="">R</i> in terms of the whole tyre hysteresis ratio <i style="">h</i> is modified by incorporating tyre radial stiffness <i style="">K</i> and rewritten as <i style="">R = L² </i>(<i style="">h/K</i>)<i style="">. </i>(<i style="">w/A</i>)<i style="">, </i>where <i style="">w</i> and <i style="">A</i> are footprint dimensions. Tyre inflation pressure <i style="">p</i> influences the magnitude of <i style="">h</i> and <i style="">K</i>. The primary objective of the present study is to obtain quantitative expressions relating <i style="">h</i> versus <i style="">p</i> and <i style="">K</i> versus <i style="">p</i>. Three P195/75R14 size radial tyres are selected for the present investigation. The <i style="">h</i> and <i style="">K</i> values of these tyres are measured as a function of <i style="">p</i> and analyzed by invoking two limiting structural terms, viz., structural hysteresis ratio <i style="">h</i>(0) and structural radial stiffness <i style="">K</i>(0)<i style="">.</i> The empirical relation between <i style="">h</i> and <i style="">p</i> is found to be inversely related as <i style="">h = k </i>(<i style="">1/p^x</i>). The <i style="">h</i>(0) values are about 0.38, 0.27 and 0.28 for tyres 1, 2 and 3. The hysteresis ratio reduction factor <i style="">h</i>(<i style="">f</i>) is normalized with respect to <i style="">h</i>(0) and is found to be about 78% of <i style="">h</i>(0) value of the respective tyre. The <i style="">K</i> term is partitioned into structural stiffness <i style="">K</i>(0) and inflation pressure stiffness <i style="">K</i>(<i style=""><img src='/image/spc_char/alpha.gif' border=0></i>)<i style="">.</i> The <i style="">K</i>(0) values are about 60, 25 and 67 N/mm respectively. The <i style="">K</i> versus <i style="">p</i> relation can be expressed as <i style="">K</i> = <i style="">K</i>(0) + <i style="">m.p.</i> = <i style="">K</i>(0) + <i style="">K</i>(<i style=""><img src='/image/spc_char/alpha.gif' border=0></i>). The pressure stiffness <i style="">K</i>(<i style=""><img src='/image/spc_char/alpha.gif' border=0></i>) is directly proportional to <i style="">p</i> as <i style="">K</i>(<i style=""><img src='/image/spc_char/alpha.gif' border=0></i>) = 0.56.<i style="">p</i>. These empirical equations with experimentally determined fitting coefficients <i style="">k</i>, <i style="">ϰ</i> and <i style="">m</i> for the three P195/75R14 tyres are presented. This study indicates that the tyre size primarily controls the magnitude in reduction of <i style="">h</i>, through <i style="">h</i>(<i style="">f</i>), and the increase in <i style="">K</i>, through <i style="">K</i>(<i style=""><img src='/image/spc_char/alpha.gif' border=0></i>), with <i style="">p</i>. The total tyre load of 5337 N is separated into structural load and pressure load; the former load has a direct relationship with <i style="">R</i> while the latter has an inverse relation. This is a new analytical approach relating tyre load and rolling loss. </smarttagtype></smarttagtype>