Calculate flatness using a set of points

[chetanchimate]

I want to find the flatness error manually without using computer. The least square method is what most CMM software use (and also ISO 1101 standard) to calculate flatness error.

I have 'n' number of points. Pi = (Xi, Yi, Zi) where i = 1, 2, 3 ... n

I fit a least square plane ax + by + cz = d and calculated distance of all points from the LS plane. eventually found the farthest point on each side of LS plane.
Flatness = [mod(max +ve) + mod(max -ve)]

However, this method is tedious to perform all calculations manually (using calculator).

Is there any easier method to find the flatness using the co-ordinate information of a set of points?

As an example, I used below five points:

P1= (11.5, 7, 1.1)
P2= (18.5, 6.9, 1.03)
P3= (4.5, 13, 1.02)
P4= (25.5, 30, 1.03)
P5= (11.5, 37.5, 1.02)

I know there is another way using minimum zone evaluation. I dont know how to use it with manual calculations.

Any thoughts?


PS: I am looking for an easier way. And by the way, flatness has no datum references, so we can not just calculate using only z co-ordinates.

 

[3DDave]

It's a curious problem to solve - to have access to a CMM and not have access to a microprocessor. It looks like most MZE methods require thousands to millions of iterations to come to an answer, so pencil and paper will not be suitable.

I suspect if there was a known shortcut it would have been published by now and would have applications in a variety of fields beyond D&T validations.

 

[AbidingDude]

My apologies if this is grossly insufficient, but, I'm still relatively new to this stuff.

I've been using a lot of statistics to verify my measurements. I would use a height gauge to measure various points. Use a statistics-capable calculator, then compare x-bar to the nominal height, and use standard deviation to determine flatness - i.e. if standard deviation is less than flatness-callout value, it should be okay.