A surface grinding operation is used to finish a flat plate that is 5.50 in wide and 12.500 in long. The starting thickness is 1.085 in. After grinding the surface, the thickness is 1.000 in. The grinding wheel had a starting diameter of 6.013 in and a width of 0.50 in. After the operation, the diameter of the grinding wheel is 5.997 in. Determine the grinding ratio in this operation.

77.40

Explanation:

Initial width = 5.5 Inches

Initial length = 12.5 inches

Initial thickness = 1.085 inches

After grinding

Thickness of flat plate  = 1 inch

Grinding wheel

starting diameter( di )= 6.013 inches

width of grinding wheel = 0.5 inch

After operation

Diameter of grinding wheel ( df ) = 5.997

Calculate the grinding ratio in this operation

First step : determine the volume of material removed from flat plate

= Length of flat plate * width of flat plate * change in thickness

= 12.5 * 5.5 * ( 1.085 - 1 )

= 5.8437 in^3

Volume of material from grinding wheel

= π / 4 * ( di^2 - df^2 ) * width  

= π / 4  * ( 6.013^2 - 5.997^2 ) * 0.5

= 0.0755 in^3

Finally the Grinding ratio

= 5.8437  / 0.0755

= 77.4

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