Centerline tangent-point deviations are important because they represent the best set of points along the centerline to qualify the shape of a tube.

Centerline tangent points are important points used to qualify tube shapes when they are compared to the master part shapes.

In tube fabrication, a tangent point is a centerline point where a straight section meets a bend. These are considered the best points for qualifying a tube shape because they form two end points that best represent the positions of each straight cylinder in space.

If you double the tangent-point tolerances and deviations, then the values correspond to a GD&T profile tolerance. VTube-LASER tangent-point tolerance envelopes are spherical radius true positions from the centerline tangent points. GD&T profile tolerances apply to the entire diameter.

For example, a GD&T profile tolerance of 3 mm is identical to a VTube-LASER tangent-point tolerance envelope of 1.5 mm.

COMPARE XYZ Tangent-point Deviations to XYZ Intersection Point Deviations

Centerline XYZ intersection points (not the same as centerline XYZ tangent points) are sometimes used for tube shape qualification.

However, intersection points are not a good choice for tube-shape qualification because:

• Intersection deviations tend to exaggerate the deviations mathematically. The exaggeration increases as the bend angle approaches 0° or 180 °. In both situations, the deviation exaggeration increases as the intersection centerlines approach parallelism.
   
• Bend angles that approach 180-degrees create the most exaggeration because intersection point deviation grows as the intersection point leaves the tube space.
  
  This is the nature of polar geometry. One degree of change at 10 mm is 0.17 mm. One degree of change at 1000 mm is 17.45 mm.
  
  Tangent points don't have this problem, because they are always closely connected to the straight sections of the tube shape.

A Visual Example of the Problem With Using Intersection Points for Qualification

See these two images to help understand the problem with using intersection points for qualification.

The white tube is the MASTER part. The pink tube is the MEASURED ALIGNED part. The blue envelopes are the tolerance envelopes for this tube qualification.

The two tangents show 0.054 and 0.046 inches in deviation. It's easy to see that the pink straights are well inside the blue envelopes. This part qualifies according to the tangent-point deviations.

However, the intersection points are separated by 0.332 inches.

The intersection deviation is 6 times the tube's profile deviation.

Therefore, intersection deviations do not act as a good representative of the actual surface profile deviation. (It is possible to overqualify a part using them.)

See VTube Intersection Point Tolerances for more information about intersection deviations.

The Tangent chart is represented by a grid of straights for each row with tangent points and midpoints for each straight:

• T1 = Tangent 1 Deviation
• MP = Midpoint Deviation
• T2 = Tangent 2 Deviation
• T1t = Tangent 1 Deviation Tolerance
• MPt = Midpoint Deviation Tolerance
• T2t = Tangent 2 Deviation Tolerance
   

Note that the two endpoints are also included in the tangent charts and reports (T1d in straight 1, and T2d in the last straight). They are an exception to the technical tangent definition given above because there is no bend attached to these points. But these points still have value in determining if the part is the correct shape, so it is convenient to include them in this chart and grid - even though they are not really tangents.

Midpoint deviations are always less than the highest corresponding tangent deviation, and higher than the lowest corresponding tangent deviation. They are included in traditional reports so that you can have three separate deviation tolerances in a straight. (T1-MP-T2)

The image on the right shows the visual representation of the chart and report above. The deviations in the grid match the part in the image. The part is made transparent so that you can see the two centerlines inside the tube. (It's easy to make parts transparent by setting the transparency value to about 0.75 inside the Parametric Tube control menu under Models.)

In this case, the T1d value is 0.9mm for straight 2.

However, the end length is 90.2mm too long.

In this application, the customer bent the part 90mm too long on purpose in order to give the bend arm clamp die enough material on the first straight to grip.

Notice that, even though the part is significantly too long, the BEST FIT algorithm didn't use the actual measured endpoint in the alignment. The alignment was based on the trimmed point on the measured centerline that was nearest the master endpoint.

So, in this case the part shape in space is qualified - but it needs trimming by 90.2mm to also qualify the end length (another critical qualifier).