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# Tolerable Tangent Deviation for NC Milling

IP.com Disclosure Number: IPCOM000112727D
Original Publication Date: 1994-Jun-01
Included in the Prior Art Database: 2005-Mar-27
Document File: 4 page(s) / 82K

IBM

## Abstract

Curved surfaces are discretized in straight lines for NC Milling. Descretisation depends upon the machining tolerance. Therefore the final surface is facetted.

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Tolerable Tangent Deviation for NC Milling

Curved surfaces are discretized in straight lines for NC
Milling.  Descretisation depends upon the machining tolerance.
Therefore the final surface is facetted.

Three cases of transition of adjacent surfaces are:

o   Both surfaces convex (mnemonic C),

o   one surface flat and the other convex (mnemonic J),  and

o   one surface convex and other concave  (mnemonic S).

After milling, the transition of adjacent surfaces is not
perceptible even if the original surfaces are not perfectly tangent
to one another, if the tangent deviation at the transition is less
than the criteria defined in this disclosure.

Geometrical Principles - The angle (A) of the facet is a function of
the machining tolerance (t) and the radius of curvature (R), when
R>>t, which is normally the case:

Sin(A) = SQRT(2t/R)

Approximating for small values of (A):

Sin(A) = A in Radians = (180/pi)xSQRT(2t/R) in degrees.

Theoretical Tangent Deviation -

For the three transitions C, J and S:

1.  Tolerable Tangent Deviation for C Transition is:
+/- (180/pi)x2x((SQRT(2t/R1)) - (SQRT(2t/R2))) in degrees
where t, R1 and R2 are in mm.

2.  Tolerable Tangent Deviation for J Transition is:
+/- (180/pi)x2x(SQRT(2t/R)) in degrees
where t and R are in mm.

3.  Tolerable Tangent Deviation for S Transition is:
+/- (180/pi)x2x( (SQRT(2t/R1)) + (SQRT(2t/R2)) ) in degrees
where t, R1 and R2 are in mm.

Factors for Catia NC - CATIA NC algorithm uses only approximately 90%
of the tolerance.

The factor: (180/pi)x2 is therefore corrected to: (180/pi)x2x(SQRT
0.9)

The Table shows the corrected factors with the machining tolerance

-----------------------------
t (mm)        :  Factor
-----------------------------
1.000         :    154
-----------------------------
0.100         :     48
-----------------------------
0.025         :     24    <=== Most often used value
-----------------------------
0.010         :     15
-----------------------------
0.001         :      4.8
-----------------------------

Examples for Catia NC:

1.  "C Type" Transition:

Two adjacent convex surfaces have at the transition the
radius of 100 mm and 25 mm respectively.  They are milled with a
machining tolerance of 0.025 mm.

We wish to know the maximum allowable tangent deviation so
that after milling the transition is still smooth.

The factor is 24 from the table.

Max angle is given by:

...