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Flatness calculation 2
- Thread starter UchidaDS
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- Thread starter
- #3
What I would like to know is how to compute the data points from the reading and compute it to flatness.
For example, my reading from a height gage is:
.2012, .2011, .2011, .0213, .2014, .2010, .2012, .2010, .2013....
Not sure what do you mean by points with flatness tolerance. Are you talking about the instrument uncertainty, granite flatness, etc?
Assuming the part is perfectly/ideally flat to the reference plane, etc.
For example, my reading from a height gage is:
.2012, .2011, .2011, .0213, .2014, .2010, .2012, .2010, .2013....
Not sure what do you mean by points with flatness tolerance. Are you talking about the instrument uncertainty, granite flatness, etc?
Assuming the part is perfectly/ideally flat to the reference plane, etc.
pmarc
Mechanical
- Sep 2, 2008
- 3,240
While flatness tolerance seems to be one of the easiest geometric tolerances to interpret and understand, it is not that easy when it comes to evaluation of actual flatness error.
Even for your seemingly simple numbers it is difficult to say anything about flatness error without employing some sort of numerical analysis. The aim of the analysis should be to find the minimum possible distance between two perfectly parallel planes unconstrained in location and orientation to any datum(s), within which all inspected points lie. This may be .0004, but does not have to (and most likely won't be).
This could even be .0000, if your readings were something like this (assuming x and y were grid coordinates and z was the height gage reading):
point #1 - x=.0000; y=.0000; z=.2010;
point #2 - x=.0000; y=.5000; z=.2010;
point #3 - x=.0000; y=1.0000; z=.2010;
point #4 - x=.5000; y=.0000; z=.2012;
point #5 - x=.5000; y=.5000; z=.2012;
point #6 - x=.5000; y=1.0000; z=.2012;
point #7 - x=.0000; y=.0000; z=.2014;
point #8 - x=1.0000; y=.5000; z=.2014;
point #9 - x=1.0000; y=1.0000; z=.2014.
Even for your seemingly simple numbers it is difficult to say anything about flatness error without employing some sort of numerical analysis. The aim of the analysis should be to find the minimum possible distance between two perfectly parallel planes unconstrained in location and orientation to any datum(s), within which all inspected points lie. This may be .0004, but does not have to (and most likely won't be).
This could even be .0000, if your readings were something like this (assuming x and y were grid coordinates and z was the height gage reading):
point #1 - x=.0000; y=.0000; z=.2010;
point #2 - x=.0000; y=.5000; z=.2010;
point #3 - x=.0000; y=1.0000; z=.2010;
point #4 - x=.5000; y=.0000; z=.2012;
point #5 - x=.5000; y=.5000; z=.2012;
point #6 - x=.5000; y=1.0000; z=.2012;
point #7 - x=.0000; y=.0000; z=.2014;
point #8 - x=1.0000; y=.5000; z=.2014;
point #9 - x=1.0000; y=1.0000; z=.2014.
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2
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pmarc
Mechanical
- Sep 2, 2008
- 3,240
UchidaDS,
Although I made a typing mistake in point #7 coordinates (there should be x=1.0000, not x=.0000), you got it right - I was indeed thinking about situation when surface was perectly flat (based on data gathered), but inclined to the basis.
It is true that the Least Squares Method (LSQ) is one of the algorithms used to evaluate actual amount of flatness error. Software finds a least squares reference plane, unrelated to any datum(s), that is a plane such that the sum of the squares of the local flatness deviations is a minimum, and based on a difference between maximum positive and negative local flatness deviations (measured in a direction normal to that least square reference plane) value of actual flatness error is computed - see Figure 4 in the attachment*.
The other method is the one already mentioned by me, called the Minimum Zone Method. Software finds two parallel planes unrelated to any datum(s) (one lying outside of material of measured surface, the other lying inside of material of measured surface) being at least possible separation. This separation is the amount of actual flatness error of measured surface - see Figure 3 in the attachment*.
For your surface being "in the same level" both methods can be used, and - as you may expect - different results may happen depending on method chosen.
* - Both figures are taken from ISO/TS 12781-1:2003.
Although I made a typing mistake in point #7 coordinates (there should be x=1.0000, not x=.0000), you got it right - I was indeed thinking about situation when surface was perectly flat (based on data gathered), but inclined to the basis.
It is true that the Least Squares Method (LSQ) is one of the algorithms used to evaluate actual amount of flatness error. Software finds a least squares reference plane, unrelated to any datum(s), that is a plane such that the sum of the squares of the local flatness deviations is a minimum, and based on a difference between maximum positive and negative local flatness deviations (measured in a direction normal to that least square reference plane) value of actual flatness error is computed - see Figure 4 in the attachment*.
The other method is the one already mentioned by me, called the Minimum Zone Method. Software finds two parallel planes unrelated to any datum(s) (one lying outside of material of measured surface, the other lying inside of material of measured surface) being at least possible separation. This separation is the amount of actual flatness error of measured surface - see Figure 3 in the attachment*.
For your surface being "in the same level" both methods can be used, and - as you may expect - different results may happen depending on method chosen.
* - Both figures are taken from ISO/TS 12781-1:2003.
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