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Apparent Intersection Measurement

Apparent Intersection Measurement

I need to measure the apparent intersection of a conical surface intersecting a flat plane surface.  I've built a jig which I can use to secure in place to fit the geometry, then measure the sharp corner intersection.  It works reasonably well, but is somewhat cumbersome and does not work for the inside corners.  

I'm looking for a tool or method accurate to within 0.010" or better.  

I've attached 3 pictures of the measurements I'm trying to take.  Both 3" and 4" dimensions are what I'm trying to do.  The corner radii are not very accurately made and cannot be used to reference really.


Does anyone know of a method or tool to make this measurement?



Matt Smith
Mechanical Engineer
'04 RHIT Grad

RE: Apparent Intersection Measurement

What is an "apparent" intersection?

Never heard the term.

RE: Apparent Intersection Measurement

The way we used to do it is cast the section with a non-shrinking material (resin), cut and grind the section into a half section based on some diameter e.g. the outside diameter of the part. Make a 25:1 or 50:1 transparent drawing of the part and pin it to a shadograph, put the cross section of the part on the bed of the shadograph and away you go. But keep in mind, we were looking for tenth's here.

RE: Apparent Intersection Measurement

if the blend radius isn't well defined, why do you need such a high accuracy ?

how about applying paint to the surface of the cone, then offering it up to the mating piece and see where the paint transfers ?

i'm assuming that the cone is defined, and not a cone of some (unknown) radius.

RE: Apparent Intersection Measurement

The apparent intersection is the dimension where two lines would intersect if there were no radius on a corner.

Matt Smith
Mechanical Engineer
'04 RHIT Grad

RE: Apparent Intersection Measurement


In your method, must I section the finished piece in order to make the measurment?  I'm not familiar with a shadograph.

RE: Apparent Intersection Measurement

how far would you get filling in the radius with plasticine ?

where is the cone centered with respect to the plate ?  
if you can locate the cone with respect to the upper surface of the plate, then reasonably simple math will determine the section of the cone on a plane at the lower surface of the plate, which would show you the "apparent" gap with your hole diameter.

RE: Apparent Intersection Measurement


The radius and surfaces being measured vary in size quite a bit (+/-0.020").  The radius is easy enough to measure with a radius gauge.  I really need to know what the dimension at the intersection is, ie. the size of the conical section.

Yes, the conical section is defined, but varies in size quite a bit.  I've considered different templates and a visual approach to see where/when it touches (similar to your paint technique) but this would require several templates.  I have many different sizes to measure, so this ends up being a lot of templates.

RE: Apparent Intersection Measurement

sorry, now i'm confused.  your previous post said you are interested in the geometyy as though the radius wasn't there; and now we're talking about the radius again.

i was looking at a math solution.  if you can define the cone with respect to the upper surface, then you can determine the section of the cone at the lower surface.  and the difference between this and the nominal hole diameter (without the fillet rad.) would give you the "apparent" gap.

if you are trying to set up to achieve a gap, could something like a "feeler" gauge (like is used with spark plugs) help ?

if you're trying to set-up the cone to achieve a gap, you could set-up the problem with math ... parameters ... cone taper angle, hole diameter, fillet radius, plate thickness; output ... position of the cone to achieve a gap of x" (gap could be defined in the plane of the lowere surface of the plate, or normal to the side of the cone).

maybe autocad could help you with this geometry ?

RE: Apparent Intersection Measurement

Do you want to know where the theoretical edges of the conical shape are?  Relative to what?  The resultant theoretical cone base diameter?  Use geometry.  Perhaps a large precision ball set in the generated conical surface and measure distance from top of the ball/sphere to surface of the part and relate that to the cone dimension.


RE: Apparent Intersection Measurement

A larger template and then measurment with feeler gauges may work.  I had not thought of that.  

We make pieces which have this type of geometry on each part.  One female mates with one male.  We have a gap between them which is filled during product use.  I am trying to study this gap size based on knowing the size of each conical section etc.  

I know what size each of the conical sections are designed to be etc. but want to know what the actual size of these conical sections are throughout a run of parts.  So, I thought the best way to characterize these was to be able to measure these two apparent intersections.

Matt Smith
Mechanical Engineer
'04 RHIT Grad

RE: Apparent Intersection Measurement

it seems to be a pretty poor process for a critical dimension (the gap) to depend on a poorly defined radius; but i guess it is what it is ?

it seems that you have to choose a cone to match a plate.  if so, i think math (or autocad) might be the best ways to approach the problem.  it seems to me that the apparent gap (as you've defined it, with repsect to the un-radiused hole) isn't much help.  you're flowing "product" between the cone and the plate, so i think you're most interested in the clearence between the cone and the hole along a normal to the cone's surface (i suspect you want a normal from the cone's surface that passes through the center of the fillet rad, ie normal to both surfaces).  this is something math can solve ... the cone's normal is inclined to the horizontal by the cone's taper angle, you want the cone's surface to intersect the normal a distance of a fillet rad + the gap from the fillet rad center, and so you've just defined the cone; you might use knowledge that there are a limited number of cones, ie a limited number of taper angles, and so a limited number of solutions.

btw, how do you control flow of the "product", assuming it changes with temperature, humidity, etc ?

RE: Apparent Intersection Measurement

All I'm trying to say is that the actual radius is inconsequential to the measurement, it changes a bit during manufacture, so I do not want to reference or try to measure to the radius.  

There's nothing flowing between the gap.  The gap is there and is filled with putty type of compound when in use.  

All I'm looking for is a good way to measure where a conical surface intersects a bisecting plane.  This would normally form a circle which could easily be measured with calipers.  In this instance, there is a radius at this corner, so this circle can no longer be measured.  So how do you find what that apparent intersection is on an actual part?

RE: Apparent Intersection Measurement

ok, why not just measure the diameter of the cone on the plane of the lower surface of the plate ?  since you know the diameter of the hole, you'd know the "apparent" gap.

RE: Apparent Intersection Measurement

I don't know the actual diameter of any part of the cone.  That's exactly what I'm trying to measure.  I know what is should be, but not what it actually is.   

RE: Apparent Intersection Measurement

parallel rulers

RE: Apparent Intersection Measurement


In your method, must I section the finished piece in order to make the measurment?  I'm not familiar with a shadowgraph.
No, of course not, that was the whole idea: trying to get accurate dimensions of a contoured part without destroying it. You'll find shadowgraphs in any better Tool & Die shop, however, due to the need to mold every part to be inspected that method doesn't really lend itself to production inspection and it is, therfore, mainly used to inspect tooling to make the parts.

RE: Apparent Intersection Measurement

But, to continue what I said previously, your best bet would be to find a shop with a Coordinate Measuring Machine that can be programmed for your part. That spits out the required dimensions in no time.

RE: Apparent Intersection Measurement

Why do you need to measure the apparent intersection?  There are better ways to measure the location and size of a cone.  What about GDT, e.g. surface profile?  You could also check diameter and location at given depth.

RE: Apparent Intersection Measurement

The top circle seems fairly easy.
You make a small thickness test cone whose slope is slightly greater  than the nominal cone slope.
Drop it into the female piece and with the aid of a depth gauge you get the height of the top of the piece to datum from which by some math you get the circle.

Next, make up a smaller cylindrical test piece whose diameter is slightly greater than the smallest diameter of the female hole;  drop it into the cavity . measure its height - to- datum and from the test piece thickness and the 2 heights you get the slope of the female cone.

Knowing the height of the female piece and the calculated slope, you get the small diameter intersection.

The male piece can be handled similarly.  

RE: Apparent Intersection Measurement

Make a sharp edged gage disk, diamter 3.500in., thickness .750in. so the gage is always above the part surface.  Set the disk in the female cone.  Measure the distance from the top of the gage disk to the part surface.  By geometry D = dg + 2*lg - 2*y.  The variation of D will be twice the variation of y, so y must be measured to less than .005in. for calculating D to .010in..

D is the large diameter of apparent intersection at the part surface
dg is the diameter of the gage
lg is the length of the gage
y is the measured distance of the gage above the part surface

Do a similar method with a gage ring for the male part.


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