Create Abbott-Firestone curve and calculate Rk family values.

PURPOSE
This app can be used to create Abbott-Firestone curve and calculate Rk, Rpk and Rvk values. Abbott-Firestone curve is also called Bearing Area curve (BAC) or Material Ratio curve.
INSTALLATION
Download the file Abbott-Firestone_Curve.opx, and then drag-and-drop onto the Origin workspace. An icon will appear in the Apps Gallery window.
NOTE: This tool requires OriginPro.
OPERATION

1. Make a worksheet active. Click Abbott-Firestone Curve app icon in Apps Gallery window.
2. In the opened dialog, select XY data for roughness input data.
3. Click OK button. A graph with a Abbott-Firestone curve and a table for Rk family values will be created.

SAMPLE OPJU FILE
This app provides a sample OPJU file. Right click on the Abbott-Firestone Curve icon in the Apps Gallery window, and choose Show Samples Folder from the short-cut menu. A folder will open. Drag-and-drop the project file BACEx.opju from the folder onto Origin. The Notes1 window in the project shows detailed steps.
Note: If you wish to save the OPJU after changing, it is recommended that you save to a different folder location (e.g. User Files Folder).

ALGORITHM

1. Calculate the empirical cumulative distribution function for the roughness data, and create the bearing area curve.
2. Find the 40% segment of the curve which is the flattest and has the smallest absolute slope.
3. Fit the 40% segment with a linear function, extend the line to x=0% and 100% and denote two end points with P₁ and P₂. Draw two horizontal lines from P₁ and P₂ respectively, and intersect with the bearing area curve at P₃ and P₄.
4. Draw two straight lines from P₃ and P₄ respectively, intersect with the vertical axes for 0% and 100% at P₅ and P₆, so that the area of the triangle P₁P₃P₅ equals to the area between the horizontal line P₁P₃ and the the bearing area curve, and the same rule for the triangle P₂P₄P₆.
5. Core Roughness Depth, Rk, is the vertical distance between two horizontal lines P₁P₃ and P₂P₄.
   Reduced Peak Height, Rpk, is the height (P₁P₅) of the upper left triangle.
   Reduced Valley Depth, Rvk, is the height (P₆P₂) of the lower right triangle.
   Material Ratio 1, Mr1, is the x value of P₃.
   Material Ratio 2, Mr2, is the x value of P₄.
   

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