Angularity Calculation GD&T Training

[pverostko]

Hello Everyone,


First time poster here, while I have used this site as a resource for my GD&T needs, I have an issue I am unable to solve and wanted to reach out to the community.


I have been working on a project to develop a standalone fixture (offline gage as we call it) that will measure the angularity of an assembled part. Traditionally, this measurement has been verified on our CMM, but due to machine availability, we need to pursue other means of checking angularity.


This fixture has been designed to output via a digital protractor, the angle between two planes defined on our assembled part. Our assembly drawing (ZF) notes the tolerance in degrees. The final assembled drawing (ZG) notes the orientation of these planes in angularity.


My question is, how exactly is angularity calculated from a given angle or more precisely, the deviation of the angle from nominal. Our Calypso reports output both deviation from nominal, i.e. 0.3298, and an angularity of 0.1962.


I understand the concepts of angularity defining a set of planes surrounding nominal, but I don’t understand how angularity is calculated. I have been successful in estimating this calculation using regression line analysis, but management seems to be stuck on the notion of an exact calculation. While this may be possible (or not), it is beyond the scope of my dealings with GD&T basics.


If someone could enlighten or point me in the correct direction it would be greatly appreciated.


Please let me know if you have any additional questions. Thanks in advance.


Paul

[Kelly_Bramble]

This fixture has been designed to output via a digital protractor, the angle between two planes defined on our assembled part. Our assembly drawing (ZF) notes the tolerance in degrees. The final assembled drawing (ZG) notes the orientation of these planes in angularity.

My question is, how exactly is angularity calculated from a given angle or more precisely, the deviation of the angle from nominal. Our Calypso reports output both deviation from nominal, i.e. 0.3298, and an angularity of 0.1962.

GD&T angularity tolerance is very different from a tolerance given in plus or minus degrees. Unless the measured surface has perfect form I don't believe it would be feasible to measure and then calculate the angularity tolerance using a digital protractor.

It is possible to measure and calculate a GD&T angularity tolerance with a protractor if the tolerance is specified on a surface with a Tangent Plane modifier or with "Each Element" specified.

A protractor when placed against the surface will contact the part surface at three of the outermost surface locations relative to the protractors contacting surface. The inner most surface locations of the plane cannot to be determined therefore the angularity cannot be determined.

An angularity tolerance defines two tolerance boundaries separated parallel to each other at the tolerance number specified within the feature control frame. The two angularity tolerance boundaries are then oriented at the basic angle (TED) relative to the specified datums. All elements of the as-built surface must fall between these two tolerance boundaries.

Ideally, in an open setup one would orient the part with respect to the datum(s) so that the surface requiring measurement is parallel to the measuring motion of a surface dial indicator. All (most) surface elements are then measured and the outermost and innermost surface elements are determined. The difference between the outermost and innermost surface elements measured is the as-built angularity.

Hopefully the measured angularity is equal or less then the specified angularity.

[pverostko]

Hello Kelly,

Thank you for the reply. Sorry I didn’t respond sooner as I have been trying to grasp this issue.

I checked, and can confirm the angularity callout has no Tangent Plane modifier. The more I look into this issue, I believe the true concern is the mating angle between two components. However, this is called out in our print as angularity for some reason. There seems to be no interest in the datum form, relative to the angularity callout in the traditional sense.

As you noted this surface should be measured with a dial indicator parallel to the datum surface in question. However, in our case we are actually mating our datum to be measured with another adapter to assists in providing the deviation from nominal (using the protractor). It seems I have lit a bit of a fire concerning this topics and has since been escalated to the design team to interrupt the true meaning of the callout.

Concerning the calculation, I have complied historical data based on CMM outputs and have determined a slope intercept. Additionally we used an excel function TAN(RADIUS(Ref dim provided by CMM)X deviation from nominal angle to accurately convert angle to angularity. While this method may be crude, between the two we have 99% confidence level of the conversion BASED on calypso calculations.

This seems to be a very interesting situation. I’m sure I have not described it well. I am almost certain as well we are really not interested in angularity but the deviation from nominal angle. It will be interesting to see where this topic goes in the near future. Hopefully I will have a confirmed answer in the next few weeks.

Again, I want to thank you for the information. If you have anything else to add please chime in. Thanks again.

Paul

[Kelly_Bramble]

If your engineering drawing specifies an Angularity - that is what you should measure for..

Below, is an image out of my GD&T Training book for quality and inspection - Geometric Metrology, Dimensional Tolerance Inspection.

Top illustration - Bottom surface is specified as Datum A and the surface at the 20 degrees basic (TED) angle has an Angularity tolerance of .13 relative to datum A.

The bottom illustration shows a sine plate on a surface plate. Datum A surface is oriented parallel to the surface plate with the sine plate.

The Surface dial indicator moves or transverses parallel to the surface plate and measures all surface elements as shown. The angularity measured is simply the highest (tallest) surface element measured minus the lowest (shortest) surface element measured. Hopefully, the highest - lowest is equal to or less than .13.

It's that simple..

Respectfully, I have no idea what you are measuring as described.

What A CMM does:

A CMM is first setup to measure many Datum A surface elements. - The CMM is told that it is establishing a Datum. Then the CMM measures many surface points on the angularity surface and uses internal math to rotate those as-measured surface points and derive the highest and lowest surface element to report the angularity. CMM's use the math to do the work of the Sine Plate.

[Belanger]

One question that I've always had.... in order to check angularity with the sine plate method, do we need a secondary datum?

[Kelly_Bramble]

do we need a secondary datum?

No, but it sure makes the measuring setup easier. You must have noticed that I oriented the part using a non-datum surface.

There are several methods one might use to orient the part optimally to actually measure the highest and lowest surface element. Open setup methods are subject to variations. A level could have been employed to initially orient the part as well. However, the best approach for a single datum and an oblique surface is to get the two highest surface elements parallel with the reference surface plate (lowest plate that the height dial indicator slides on). A plate parallel to the reference surface plate lowered onto the part and then the part is wiggled until two of the outermost contact surface areas make contact with the parallel plate.

Of course a modern CMM would be easy money in this scenario.

If this were an actual installation we would assume that the part can rotate about datum A in the target installation. Therefore the part would likely orient itself to the most attainable surface contact elements. Therefore, during measurement we would simulate that installation scenario to properly orient the part to determine the angularity.

[Belanger]

That makes sense -- as long as datum A is set up on, then the part can be rotated. A non-datum surface can help, if that compound-angle effect is first taken away. (Kind of like checking flatness of a top surface while the part is set on leveling screws -- a non-datum surface that is first qualified for leveling.)

[pverostko]

Kelly,
I wanted to follow up with you concerning this topic. I understand your illustrations fully and appreciate the additional information you provided. I will admit, in the simple diagram you presented, the concept of angularity and how it is to be measured was well explained.
I feel that our situation was different. After discussing the issue with our company design team and development group, our situation does not follow your example. In this situation datum A for example is projected as a plane and referenced to another symmetry plane. The angularity is then calculated based upon the deviation of the datum from the reference plane.
I must admit this particular instance of GD&T goes beyond my basic knowledge of angularity. The explanation I was given is that this was another way of controlling the angle between the two planes versus using an angle tolerance. I did not argue the fact of whether the usage of angularity in this situation to control an angle was correct of not. I must state I am not a mechanical engineer nor am I part of any development team. I still do not fully understand how, if you cannot physically measure datum A, how can you tolerance a surface using angularity.
Moving forward, the design team did provide a conversion formula using basic trigonometry to convert between the two units. My question was simply a means of researching the topic. Eventually it was escalated to the design team for clarification. I do appreciate your help on this topic and wish I could provide more insight on the problem/solution.
Again, thank you for the information you provided.
Regards,
Paul