Establishment of the distribution function of the integrated surface for squeeze casting by robbe Valloire model

Greenwood and Williamson proposed a statistical description of the vertex height of rough surface and considered that the convex curvature radius of rough surface is constant. Whitehouse, Archard and Nayak proposed that the radius of the rough surface bulge also varies, not only the height of the rough surface vertex. F. Robbe Valloire proposed a more perfect method, which assumes that the rough surface bulge has a certain radius of curvature and is lognormal distribution. The average curvature radius of each bulge can be obtained from the micro geometric parameters of each “motif”. Its calculation formula is as follows,

In the formula, ρ I varies with different bulges, but its value can be determined by the above formula.

The mean radius of curvature ρ m is calculated as follows,

The corresponding root mean square of radius of curvature ρ RMS is calculated as follows,

The distribution function of curvature radius of rough surface is as follows,

Where,

F. Robbe Valloire assumes that the height of convex vertices of rough surface conforms to normal distribution. The average height of the convex vertex ZM = 0 and its root mean square is,

The distribution function of the height of the convex vertex is as follows,

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