Re-examination of the coefficient of determination (r2) using road materials engineering case studies

The analysis of scientific data is integral to materials engineering and science. The correlation between measured variables is often quantified by estimating the coefficient of determination or the r2 value. This is the recognised procedure for determining linear relationships. The authors review the derivation of the r2 value and derive an associated quantity, termed the relative deviation (RD), which is the ratio of the root mean square of the deviations about the fitted line to the root mean square of the deviations about the y bar line expressed as a percentage. The relative deviation has an advantage over the coefficient of determination in that it has greater numerical sensitivity to changes in the spread of data about the fitted line, especially when the scatter is small. In addition, the relative deviation is able to define, in percentage terms, the reduction in scatter when different independent variables are correlated with a common dependent variable. Four case studies in the materials field (aggregate crushing value, Atterberg limits, permeability and creep of asphalt) from work carried out at the Queensland Main Roads Department are presented to show the use of the new parameter RD.

Prediction of tread block forces for a free-rolling tyre in contact with a rough road

This paper describes a new approach to model the forces on a tread block for a free-rolling tyre in contact with a rough road. A theoretical analysis based on realistic tread mechanical properties and road roughness is presented, indicating partial contact between a tread block and a rough road. Hence an asperity-scale indentation model is developed using a semi-empirical formulation, taking into account both the rubber viscoelasticity and the tread block geometry. The model aims to capture the essential details of the contact at the simplest level, to make it suitable as part of a time-domain dynamic analysis of the coupled tyre-road system. The indentation model is found to have a good correlation with the finite element (FE) predictions and is validated against experimental results using a rolling contact rig. When coupled to a deformed tyre belt profile, the indentation model predicts normal and tangential force histories inside the tyre contact patch that show good agreement with FE predictions. © 2012 Elsevier B.V..

An integrated model of rolling tyre vibrations on a smooth road

We describe new results on the vibrations of rolling tyres, aimed at noise prediction for tyres of given design on a smooth road surface. This new approach incorporates our existing models, of smooth road-tyre interaction and belt vibration but includes additional features that are required for real tyre patterns. To this end, the model allows variable tread block size and grooves along the belt circumference; the density and angle of these grooves may also vary laterally. The key innovation is to treat the tyre belt as a laterally stacked series of rings, each of which is equipped with a set of viscoelastic springs around its circumference. It is shown how to use this construction to mimic the details of actual tyre patterns and, in conjunction with existing models, predict belt vibrations. The construction is applied to develop a ring discretisation for a real tyre that shows strong lateral variations. It is shown that the vibration amplitude is concentrated on a set of parallel lines in frequency-wavenumber space and that the tread pattern dictates the occurrence and spacing of these lines. Linkage to a boundary element calculation then allows quantification of the influence of tread parameters on radiated noise. Keywords: Vibration, tread pattern, tyre noise. Copyright © (2011) by the Institute of Noise Control Engineering.

YBCO single grains seeded by 45° - 45° bridge-seeds of different lengths

Single grain, (RE)BCO bulk superconductors in large or complicated geometries are required for a variety of potential applications, such as motors and generators and magnetic shielding devices. As a result, top, multi-seeded, melt growth (TMSMG) has been investigated over the past two years in an attempt to enlarge the size of (RE)BCO single grains specifically for such applications. Of these multi-seeding techniques, so-called bridge seeding provides the best alignment of two seeds in a single grain growth process. Here we report, for the first time, the successful growth of YBCO using a special, 45{\deg} - 45{\deg}, arrangement of bridge-seeds. The superconducting properties, including trapped field, of the multi-seeded YBCO grains have been measured for different bridge lengths of the 45{\deg}- 45{\deg} bridge-seeds. The boundaries at the impinging growth front and the growth features of the top, multi-seeded surface and cross-section of the multi-seeded, samples have been analysed using optical microscopy. The results suggest that an impurity-free boundary between the two seeds of each leg of the bridge-seed can form when 45{\deg}- 45{\deg} bridge-seeds are used to enlarge the size of YBCO grains.