Some thirty odd years ago I jotted down a formula to calculate the diameters of three dissimilar gage pins that when bundled together with rubber band could be used to gauge a hole of larger diameter. Recently, the need arose again and after the disappointment of searching my memory, I undertook the exercise anew. In my experience, the most common gage pin sets a machine shop will have run from .061” – .250” and .251” – .500”. These occur in a variety of tolerance classes. The following has been formulated for “minus” gage pin sets. Manipulation of applicable hole tolerances...
Continue reading...Machining
Polygonal Exclusion Zone Macro in CNC Applications | Steve Wait – December 3, 2019
A portion of the macro below (in red) is an example of hexagonal boundary membership validation. Reference prior post: CNC PARABOLOID INTERPOLATION % O01491 (PARABOLIC, METRIC) N8T8M6 (50.8mm 2FL HSS B EM) G21G40G80G90T2G187P3(/M1) (M8) /M88G54M11G0X0.Y0.M3S3750G43H1Z50.8M31G1Z25.4F1. G65P1492D50.8K312.369 (PASS VARIABLES TO MACRO) G0G28G91Z0.M89G90Y101.6M9M30% %O01492(AXIS SYMMETRIC, CONCAVE PARABOLOID, INTERPOLATION MACRO) #1=1/[4*#6] (A, COEFFICIENT) #3=0. (INITIALIZE RADIAL DISPLACEMENT OF PARABOLA X COORDINATE IN XZ PLANE) #4=.0005 (RADIAL INCREMENT OF X COORDINATE) #5=0. (INITIALIZE ANGULAR DISPLACMENT OF THETA IN XY PLANE) #8=.3 (ANGULAR INCREMENT OF THETA IN XY PLANE) N1#3=#3+#4 (NEXT RADIAL DISPLACEMENT OF X COORDINATE IN XZ PLANE) #5=#5+#8 (NEXT ANGULAR DISPLACEMENT OF THETA...
Continue reading...CNC Paraboloid Interpolation | Steve Wait – April 26, 2019
The fundamentals of CNC machining require an intimate familiarity with linear ( G1 ) and circular ( G2 / G3 ) interpolation and the application of cutter compensation ( G41 / G42 ) used to produce an offset or parallel tool path. Parabola interpolation, applicable to tool center line via a standard form equation, is easy enough using a Fanuc style B Macro. Unfortunately, a standard CNC control does not possess the ability to apply cutter compensation to such a tool path. And, unlike a line or circle, a parallel path to a parabola is not simply an offset of...
Continue reading...Three-Dimensional Compensation to the Paraboloid | Steve Wait – April 5, 2019
z = ax2 (xz plane) a = coefficientF = .25a = focus (focus to vertex)D = ball diameterx = x coordinate on parabola (in xz plane)Xc = x compensated, rotationally transformed value (ball center)Yc = y compensated, rotationally transformed value (ball center)z = z coordinate on parabola (in xz plane)Zc = z compensated, (ball center)θ = angular displacement (in xy plane) Paraboloid 3D Compensation Equations (Ref. Fig. 1) Xc = cos θ (x ± (xD / (2√(4F2+x2)) Yc = sin θ (x ± (xD / (2√(4F2+x2)) Zc = z ± (FD / √(4F2+x2)) Fig. 1
Continue reading...Offset or Parallel Path to the Parabola | Steve Wait – April 4, 2019
y = ax2 (xy plane) a = coefficientk = .25a = focus (focus to vertex)d = twice the desired parallel or offset amountx = x coordinate on parabolaXc = x offset valuey = y coordinate on parabolaYc = y offset value Parabola Offset / Parallel Path Compensation Equations (Ref. Fig. 1) Xc = x ± (xd / (2√(4k2+x2))) Yc = y ± (kd / √(4k2+x2)) Fig. 1 Geogebra animation can be viewed here: Offset or “Parallel” Curve to the Parabola – GeoGebra
Continue reading...