Inclined plane method

An inclined plane method is specified for coated fabrics in BS342439. The test piece is attached to a sled resting on an inclined plane which is covered with the other surface to be tested. The inclination of the plane is varied until sliding takes place. This is probably the simplest form of friction test but not an accurate one and, of course, cannot operate at any given velocity. 

SLIP RESISTANCE USING AN INCLINED-PLANE METHOD... 

As it is practically impossible to compare slip resistance or static coefficients of friction of various WPC materials using the same experimental approach (Table 11.3), I have undertaken—while preparing this book for the publication—a simplified comparison using the standard incline-plane method. This method is a standard experiment in mechanical physics and involves tilting a platform to the point where movement of a material first occurs. The tangent of the angle of the plane at the point of movement is equal to the static coefficient of friction. 

TABLE 11.5 Static coefficient of friction for piastic or WPC deck boards, measured using a simplified inclined plane method. All measurements were done in the most slippery directions, that is, along the grain. Date for dry and wet pressure treated lumber are given for a comparison... 

Staxing with this frictional analogy, the inclined plane method of measuring friction would gi c an apparent coefficient of friction, since conditions are not tighll) controlled (xelocilx. for example, cannot be. specified) and there is little chance of relating the result to other conditions. 

The static coefficient of friction was measure on the cured PCL flocked aluminum test samples using the inclined plane method. Starting from horizontal, the angle of the inclined plane slowly and steadily increased until the frictional surfaces begin to slide past each other. The angle of inclination at which sliding starts, q, is noted. The static coefficient of friction (ji) is then calculated from ... 

Coefficient of static friction of uncoated paper is determined by the inclined plane method. " One specimen of paper is clamped on an inclined plane and the... 

The Japanese standard contains both horizontal and inclination method in one standard. ISO specifies only the horizontal plane method, which is also used in the same form in the United Kingdom. France specifies both horizontal and inclined plane methods, and also a special procedure for printing and business paper. 

ASTM D4918-97(2007) Standard Test Method for Coefficient of Static Friction of Uncoated Writing and Printing Paper by Use of the Inclined Plane Method. 

This equation has been derived as a model amplitude equation in several contexts, from the flow of thin fluid films down an inclined plane to the development of instabilities on flame fronts and pattern formation in reaction-diffusion systems we will not discuss here the validity of the K-S as a model of the above physicochemical processes (see (5) and references therein). Extensive theoretical and numerical work on several versions of the K-S has been performed by many researchers (2). One of the main reasons is the rich patterns of dynamic behavior and transitions that this model exhibits even in one spatial dimension. This makes it a testing ground for methods and algorithms for the study and analysis of complex dynamics. Another reason is the recent theory of Inertial Manifolds, through which it can be shown that the K-S is strictly equivalent to a low dimensional dynamical system (a set of Ordinary Differentia Equations) (6). The dimension of this set of course varies as the parameter a varies. This implies that the various bifurcations of the solutions of the K-S as well as the chaotic dynamics associated with them can be predicted by low-dimensional sets of ODEs. It is interesting that the Inertial Manifold Theory provides an algorithmic approach for the construction of this set of ODEs. 

With the supposition that the slip layer is thin and the slip velocity is constant, various analyses have been developed in the search for the ideal experimental method to define slip. The Mooney analysis (20) for both tube flow and concentric cylinder flow has been applied to a wide range of materials including polymer solutions (21), filled suspensions (22), semisolid foods (23), fruit purees (24), and ketchups (25). Alternate estimates of slip velocity have been determined experimentally from, parallel plate torsion flow (26), from flow data in channels and inclined planes, and from porous medium geometries (8). 

The effects of a fabric stiffening treatment can be quantified by the cantilever method described in ASTM 01388-96. A sample of specified length and width is placed on top of the test device. The device has a horizontal surface connected to a downward incline. The fabric is pushed over the incline until the sagging leading edge just touches the inclined plane of the device. The length of fabric that has passed over the point where the horizontal and incline meet is used to calculate the fabric s flexural rigidity. 

Figure 6.6 Liquid surface tension determination by the height of a meniscus on a vertical plane method y is the coordinate on the vertical axis and R, is the two-dimensional radius of curvature in the plane of this figure. When y= 0, the pressure difference, AP = 0, and y = h at the triple-point where liquid-solid-air intersect q> is the inclination angle of the y = f(x) function and (tp= 90° - 0) at point h. The slope of the y = f(x) curve can be given as (dy/dx) = -tan tp. pL is the density of the liquid and pv is the density of the vapor.

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