Cusp height to Surface roughness in Ra calculation

[Thunderbird336]

This seems like it would be an easy thing to find the answer for but after many hours of searching I cannot come up with it. I can easily calculate the cusp height for machining a surface with a ball endmill and a given stepover but I cannot find a formula for calculating the theoretical surface finish in Ra. A coworker told me that dividing the cusp height by 4 gives the Ra and that seems to be right, it is supported by what I find from calculators on the Internet, but is it exact? And if it is right how is that an average?

I've seen a few formulas using an integral (I think, I have forgotten my calculus, unfortunately) but I can't figure out how to use that to try it. I've found simpler formulas that say something like Ra = (m1 + m2 + m3 + m4)/4 but in my case I have just one value, of course, that answer would just be the exact same cusp height.

I would sure appreciate some help with this, this keeps coming up and I feel so uneasy not understanding it.

Thanks in advance,
Gary

 

[IRstuff]

You do realize that Ra is an average, so "exact" is not a thing, here.

see:

http://www.harrisonep.com/electropo...s result in real,improvements from 10 to 35%.

The integral realistically only applies to a semi-continuous function, and it's unlikely you'd ever have that in a real measurement. For real measurements, the summation equation is used, and for a high enough density of measurements, the results should be close, but never "exact."

TTFN (ta ta for now)
I can do absolutely anything. I'm an expert!

https://www.youtube.com/watch?v=BKorP55Aqvg

faq731-376 forum1529 Entire Forum list

http://www.eng-tips.com/forumlist.cfm

 

[EdStainless]

Do you have a copy of ASME B46.1?
The title is Wave and Lay, not roughness.
There are ways to approximate an R value for a regular machined surface.
But you need to look at the base equations.

= = = = = = = = = = = = = = = = = = = =
P.E. Metallurgy, consulting work welcomed

 

[Thunderbird336]

You do realize that Ra is an average, so "exact" is not a thing, here.

Yes, I do, my question was about the theoretical surface finish calculation, I don't expect the result to be exact. I didn't want to use a formula that was just an approximation if there was something more exact. We are milling these parts in a fairly small tolerance for surface roughness so it helps to have a good starting point. It takes quite a long time to mill, check, reprogram, mill and check again. Thank you for your reply, though.

Do you have a copy of ASME B46.1?

I do not currently have one; I will start looking for one though. I bought a copy of David Whitestone's "Surfaces and Their Measurements" and it has helped get me a lot closer to the answer. Between the book and some other technical papers that I found it seems that Ra was formerly CLA or "Centerline Average". How to calculate that centerline is where I am at right now... most seem to say that it is based on the area defined by peaks and valleys. Since I am working with a ballnose endmill, that will just be two peaks and one valley comprised of a semi-circle with a known radius and depth, if I am understanding this correctly. Does this sound right to you?

Thank you for your reply.

Best regards, Gary

 

[IRstuff]

This article looks like it might be useful

Cusp height and surface roughness in z-level milling

TTFN (ta ta for now)
I can do absolutely anything. I'm an expert!

https://www.youtube.com/watch?v=BKorP55Aqvg

faq731-376 forum1529 Entire Forum list

http://www.eng-tips.com/forumlist.cfm

 

[mfgenggear]

Thunderbird336

This may or may not be useful information. there are sample gages sold that have the standard roughness. eg 250. 125. 63. 32 16. & 8
for visual reference, sold at McMaster Carr, and for actual values use a profilometer. make life easier.