## Math behind rockwell hardness measurement

I need to calculate the force of a pin impacting a solid metal. I know the shape of the indenter, the precise shape and depth of the indentation and the mechanical properties of the solid metal including modulus, yield and ultimate strength. The pin is being driven by ultrasonic wave guide so it is not simply a gravity problem.
In my mind this is the basic equation that Rockwell Hardness uses with the exception that they know the force and indenter shape and measure the depth of indentation to calculate hardness.
Does anyone know how to solve this?
Thanks

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 If you are referring to the standard Rockwell method then there are two forces that are applied, the first F0 is applied first then another load, significantly larger than the first, is applied. Considering your case you could sort out the list of indenters and their respective Rockwell notation (HRB,HRC..etc) and then look at the force value. Now I have a Rockwell table at hand over here but it is in my national language and from what I can see unless you're indenter is a 1/16 inch sphere, you're safe. Since there's pretty much about five different options with a 1/16 inch sphere.
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