مدل های رگرسیون خطی پارامترهای سطح زمین در اصطکاک بین Neolite کاشی و معدن

For slips and falls, friction is widely used as an indicator of surface slipperiness. Surface parameters, including surface roughness and waviness, were shown to influence friction by correlating individual surface parameters with the measured friction. A collective input from multiple surface parameters as a predictor of friction, however, could provide a broader perspective on the contributions from all the surface parameters evaluated. The objective of this study was to develop regression models between the surface parameters and measured friction. The dynamic friction was measured using three different mixtures of glycerol and water as contaminants. Various surface roughness and waviness parameters were measured using three different cut-off lengths. The regression models indicate that the selected surface parameters can predict the measured friction coefficient reliably in most of the glycerol concentrations and cut-off lengths evaluated. The results of the regression models were, in general, consistent with those obtained from the correlation between individual surface parameters and the measured friction in eight out of nine conditions evaluated in this experiment. A hierarchical regression model was further developed to evaluate the cumulative contributions of the surface parameters in the final iteration by adding these parameters to the regression model one at a time from the easiest to measure to the most difficult to measure and evaluating their impacts on the adjusted R2 values. For practical purposes, the surface parameter Ra alone would account for the majority of the measured friction even if it did not reach a statistically significant level in some of the regression models.

Slips and falls are a serious problem. It has been estimated that the annual direct cost of occupational injuries due to slips, trips and falls in the USA exceeded 6 billion US dollars (Courtney et al., 2001). Leamon and Murphy (1995) reported that falls on the same level, where slipperiness is one of the critical issues, accounted for 65% of claim cases and 53% of claim costs in total direct workers’ compensation for occupational injuries due to slips and falls. To prevent incidents of slips and falls, friction is widely used as an indicator of floor slipperiness. Surface texture plays a crucial role in determining surface friction, although the contact interface between shoe and floor is complex (Chang et al., 2001a). Using the hydrodynamic squeeze-film theory, Proctor and Coleman (1988) demonstrated that a certain level of surface texture is needed to increase friction. While the friction measurement related to the problems in slips and falls remains controversial, measurements of surface texture could be a reliable and objective complement to friction measurements (Chang et al., 2001a and Chang et al., 2001b). The surface textures under consideration in this paper are those on nominally flat surfaces which do not include the macroscopic floor features known as molded surface patterns or profiled surfaces. In addition to surface roughness, surface waviness might play a role in surface friction as shown by Chang et al., 2004a and Chang et al., 2004b. The profile measured with a profilometer is filtered with a selection of a filtering length, also known as the cut-off length, to obtain the surface profile of either surface roughness or surface waviness, also known as the surface heights. The cut-off length is the filtering length that is used as a reference to properly capture important surface features of interest as indicated by Whitehouse (1994). The surface roughness profile contains components with shorter wave lengths compared with the cut-off length, while the surface waviness profile consists of components with longer wave lengths. The surface parameters are calculated from the filtered profiles. The relative importance of surface roughness or surface waviness on the measured friction depends on the cut-off length used and contaminants at the interface as demonstrated by Chang et al. (2004a). Their results indicate that some of the surface waviness parameters on floors could have a higher correlation coefficient with friction measured with liquid contamination than the surface roughness parameters when a short cut-off length is used for the surface profile measurements or when the viscosity of the liquid contaminant is high. Among the surface waviness parameters evaluated, as listed in Table 1, WΔa, Wa and Wtm had strong correlations with the measured friction. The surface roughness parameters measured with a longer cut-off length would contain some of the waviness components measured with a shorter cut-off length. The surface parameters generated with different cut-off lengths reflect different characteristics of the measured surface. The viscosity of the liquid contaminants, besides tread patterns on the shoe sole surface, determines how fast the contaminants will be squeezed out of the shoe and floor interface and, therefore, how close two surfaces approach each other during the contact. The two surfaces will be closer to each other when the viscosity is low compared with the situation when the viscosity is high. Therefore, surface waviness could be more relevant to the measured friction when the viscosity is high (film remains thicker and contact is made only near the crests of the surfaces), while surface roughness could be more relevant when the viscosity is low (film is squeezed thinner and there is more intimate contact between surfaces), as confirmed by Chang et al. (2004a). Table 1. The definitions of surface parameters. Parameter Definition Surface roughness R3y Maximum height of third highest peak to third lowest valley in each cut-off length R3z Mean height from third highest peak to third lowest valley in each cut-off length Ra Arithmetical average of surface heights or the center line average of surface heights Rk Kernel roughness depth Rku Kurtosis of surface heights Rp Maximum height of the profile above the mean line within the assessed length Rpk Reduced peak height Rpm Average of the maximum height above the mean line in each cut-off length Rq Root mean square of surface heights Rsk Skewness of surface heights Rt Maximum peak to valley height in the assessed length Rtm Average of peak to valley height in each cut-off length Rv Maximum depth of the profile below the mean line within the assessed length Rvk Reduced trough depth Ry Maximum of peak to valley in all cut-off lengths S Mean spacing of adjacent local peaks Sm Mean spacing between profile peaks at the mean line λq Root mean square measure of spatial wave length Δa Arithmetical mean of surface slope Δq Root mean square of surface slope Surface waviness Wa Arithmetical average or the center line average of surface heights Wku Kurtosis of surface heights Wp Maximum height of the profile above the mean line within the assessed length Wpm Average of the maximum height above the mean line in each cut-off length Wq Root mean square of surface heights Ws Mean spacing of adjacent local peaks Wsk Skewness of surface heights Wt Maximum peak to valley height in the assessed length Wtm Average of peak to valley height in each cut-off length Wv Maximum depth of the profile below the mean line within the assessed length Wy Maximum of peak to valley in all cut-off lengths Wλq Root mean square measure of spatial wavelength WΔa Arithmetical mean of surface slope WΔq Root mean square of surface slope Table options The majority of the published studies on the effects of surface textures on friction related to slip and fall incidents have focused on surface roughness. As reported in the literature, surface roughness parameters Ra, Rtm, Rpm, Δa and Rk, as defined in Table 1, in general had strong correlations with the friction measured at the shoe and floor interface ( Chang et al., 2001a and Chang et al., 2004b). It was shown that the parameter Rtm had a strong correlation with the subjective ranking of slipperiness ( Harris and Shaw, 1988) and with the measured friction on liquid contaminated surfaces ( Manning et al., 1990 and Manning and Jones, 1994). It was demonstrated that surface parameter Ra had a strong correlation with the measured friction on surfaces contaminated with liquid ( Stevenson et al., 1989 and Grönqvist et al., 1990). Friction measured with liquid contaminants was shown to have a strong correlation with Rpm of the floor surfaces ( Chang, 1998, Chang, 1999, Chang, 2000, Chang, 2001, Chang, 2002, Chang and Matz, 2000 and Chang et al., 2004b). The measurement of Rpm on floor surfaces was recommended by Health and Safety Executive (HSE) Food Sheet 22 ( HSE, 1999). It was demonstrated that surface parameter Δa had a strong correlation with the measured friction ( Chang, 1998, Chang, 2000, Chang, 2001, Chang, 2002, Kim and Smith, 2000 and Chang et al., 2004b). It was reported that friction measured with liquid contaminants had a strong correlation with Rk of floor surfaces ( Chang, 1998, Chang, 1999, Chang, 2000, Chang, 2001, Chang, 2002, Chang and Matz, 2000 and Chang et al., 2004b). In the previously published studies on the effect of surface feature parameters on friction, the main focus was to investigate the relationship between individual surface parameters and the measured friction. Based on the results of linear correlation coefficients, surface parameters with higher correlation coefficients with friction were identified. However, collective effects of these surface parameters on the measured friction were not investigated and could provide a broader perspective on the contributions from all the surface parameters evaluated. The objective of this study was to investigate linear regression models of floor surface parameters, including surface roughness and waviness, on friction between quarry tiles and Neolite. Through regression models, the surface parameters that contribute the most to the friction measured could be identified.

This study investigated the collective input from multiple surface feature parameters as a predictor of friction using regression models which could provide a broader perspective on the contributions from all the surface parameters evaluated. The surface parameters were subdivided by their measurement characteristics and gradually eliminated from the regression model through iterative processes based on their correlation with other surface parameters and impact on the adjusted R2 value. The surface parameters Ra, Rpm, Δa, WΔq and Wtm were retained in the final iteration of the regression model. The surface parameters with statistical significance in the regression model were generally consistent with those obtained from the correlation between individual surface parameters and the measured friction for the conditions evaluated in this experiment. However, for the 8 mm cut-off length and 85% glycerol concentration, the surface parameter Δa was statistically significant in the regression model despite the fact that it had the lowest correlation coefficient with the measured friction among the five parameters in the final iteration. A hierarchical regression model was developed to evaluate the cumulative contributions of the surface parameters in the final iteration by adding these parameters to the regression model one at a time from the easiest to measure to the most difficult to measure and evaluating their impacts on the adjusted R2 values. For practical purposes, the measurement of Ra alone would be sufficient if the resources are limited. The addition of measurements of Rpm and Δa will improve the prediction of the measured friction further if additional resources are available.