Calculations

Calculations

• Points along a piece at a chord tolerance

  Sample points no farther than a tolerance from an arc, for checks and drawing.

  step angle = 2 acos(1 − tol ÷ r)

  2D curve offsets for toolpaths cam-offset.js

  • PartCraft
  64-bit

• Bounding box of a piece

  The extent of a line or arc, including where an arc bulges past its ends.

  ends, plus c ± r along each axis direction the arc passes

  2D curve offsets for toolpaths cam-offset.js

  • PartCraft
  64-bit

• Splitting a loop at distances along it

  Cuts a loop at given distances from its start, used for tabs and ramps.

  t = (cut − length so far) ÷ piece length

  2D curve offsets for toolpaths cam-offset.js

  • PartCraft
  64-bit

• Depth levels

  The heights of the passes between the top and the bottom of a cut.

  n = ceil((top − bottom) ÷ stepdown − 1e-9); z_i = top − (top − bottom)(i + 1) ÷ n; last = bottom

  2.5-axis toolpaths cam-paths.js

  • PartCraft
  64-bit

• Clearance, retract and cut heights

  The heights an operation moves at, from the stock top and the operation's settings.

  clearance = stock top + clearance; retract = min(clearance, stock top + retract); bottom = geometry bottom + offset

  2.5-axis toolpaths cam-paths.js

  • PartCraft
  64-bit

• Arc move with changing height

  Writes one line or arc as moves, splitting an arc into half turns and sharing the height change among them.

  z after a piece = z + (z₁ − z₀) × piece length ÷ arc length; last piece ends at z₁

  2.5-axis toolpaths cam-paths.js

  • PartCraft
  64-bit

• Ramp along a path

  Lowers the tool linearly while it follows a chain of lines and arcs.

  z = z₀ + (z₁ − z₀) × length so far ÷ total length

  2.5-axis toolpaths cam-paths.js

  • PartCraft
  64-bit

• Facing rows

  The positions of the back-and-forth rows that face the stock.

  n = ceil(width ÷ (stepover × d) − 1e-9); row_i = b₀ + (b₁ − b₀) i ÷ n; run from a₀ − R − overhang to a₁ + R + overhang

  2.5-axis toolpaths cam-paths.js

  • PartCraft
  64-bit

• Pocket offset levels

  The successive inward offsets a pocket is cleared along.

  level k at distance d₀ + k × stepover, until nothing is left

  2.5-axis toolpaths cam-paths.js

  • PartCraft
  64-bit

• Helix entry

  The half-turn arcs that take the tool down into a pocket at a set ramp angle.

  pitch = 2π ρ tan(angle); half turns = ceil((z_from − z) ÷ (pitch ÷ 2) − 1e-9); z after half turn i = z_from − (z_from − z)(i + 1) ÷ n

  2.5-axis toolpaths cam-paths.js

  • PartCraft
  64-bit

• Ramp entry along a loop

  How far along the first loop the tool travels while ramping down a level.

  length needed = (z_from − z) ÷ tan(angle); whole loops = floor(needed ÷ L); remainder split off the loop

  2.5-axis toolpaths cam-paths.js

  • PartCraft
  64-bit

• Contour offset

  The path of the tool center round an outline.

  d = R + stock to leave; outside: offset by −d (grow); inside: offset by +d

  2.5-axis toolpaths cam-paths.js

  • PartCraft
  64-bit

• Lead-in and lead-out arcs

  Quarter-circle arcs that bring the tool onto and off a contour through the air side.

  center = start + ρ × left normal; quarter turn ending (or starting) at the contour's start; ρ halved up to 4 times until the arc is in air

  2.5-axis toolpaths cam-paths.js

  • PartCraft
  64-bit

• Holding tabs

  Where the tool lifts over tabs that keep the part attached.

  tab k centered at (k + ½) L ÷ tabs; lifted over tab width + tool diameter; tab top = bottom + tab height

  2.5-axis toolpaths cam-paths.js

  • PartCraft
  64-bit

• Drill depth and R plane

  How deep each hole is drilled and the height the drill returns to between holes.

  through: z = bottom − breakthrough − (tip length when full diameter is asked); R = min(retract, highest stock or part near the hole + R plane)

  2.5-axis toolpaths cam-paths.js

  • PartCraft
  64-bit

• Highest point between two holes

  The highest part or stock under the drill as it moves from one hole to the next.

  max of heights at 9 points across the tool, every 1 mm along the move

  2.5-axis toolpaths cam-paths.js

  • PartCraft
  64-bit

• Chamfer depth and offset

  How deep and how far out a chamfer mill runs to cut a chamfer of a given width.

  β = tool angle ÷ 2; depth = width ÷ tan β; offset = tip radius + tip offset × tan β; z = edge height − depth − tip offset

  2.5-axis toolpaths cam-paths.js

  • PartCraft
  64-bit

• Engagement angle of adaptive clearing

  The angle of the cutter's rim in material for a set cutting width, listed with the operation.

  angle = acos(1 − min(1, w ÷ R)) × 180 ÷ π

  2.5-axis toolpaths cam-paths.js

  • PartCraft
  64-bit

• Length of a toolpath segment

  The length of a straight or helical move, used for the machining time.

  line: |b − a|; arc: √((|sweep| × r)² + Δz²)

  2.5-axis toolpaths cam-paths.js

  • PartCraft
  64-bit

• Points along a toolpath segment

  Sample points along an arc move for the simulation overlay and checks.

  step angle = 2 acos(1 − tol ÷ r); point i at a₀ + sweep × i ÷ n, z linear

  2.5-axis toolpaths cam-paths.js

  • PartCraft
  64-bit

• One-dimensional squared distance transform

  For each cell of a row, the squared distance to the nearest marked cell, by lower envelopes of parabolas.

  d(q) = min_p ((q − p)² + f(p)); parabolas meet at s = ((f(q) + q²) − (f(p) + p²)) ÷ (2q − 2p)

  Adaptive clearing passes cam-adaptive.js

  • PartCraft
  64-bit

• Distance to the nearest marked cell

  The straight-line distance, in cells, from every cell to the nearest cell of a mask.

  columns then rows of the 1D transform; distance = √(squared distance)

  Adaptive clearing passes cam-adaptive.js

  • PartCraft
  64-bit

• Grid over the region

  Lays a grid over the region and stores, per cell, whether it is inside and its exact distance to the walls.

  cell h = R ÷ 12 (× 1.25 until the grid fits); wall distance from the region's lines and arcs

  Adaptive clearing passes cam-adaptive.js

  • PartCraft
  64-bit

• Contour of the distance field

  Traces the line where the field crosses zero, which becomes a pass.

  crossing on a cell edge at t = a ÷ (a − b)

  Adaptive clearing passes cam-adaptive.js

  • PartCraft
  64-bit

• Field whose contour is the next pass

  Sets up the field that is zero where the tool center cuts the set width into the remaining material.

  F = (R − w) − distance to material (allowed cells); positive elsewhere

  Adaptive clearing passes cam-adaptive.js

  • PartCraft
  64-bit

• Keeping passes off the walls

  Moves any pass point that came nearer the walls than the tool radius plus stock to leave.

  p ← nearest wall point + unit(p − nearest) × (R + leave + 1e-6)

  Adaptive clearing passes cam-adaptive.js

  • PartCraft
  64-bit

• Simplifying a pass

  Drops points of a pass that lie within a tolerance of the line between their neighbors.

  keep the point farthest from the chord when its distance > cell ÷ 4, then repeat on both halves

  Adaptive clearing passes cam-adaptive.js

  • PartCraft
  64-bit

• Marking what a pass clears

  Marks every grid cell the tool covers along a pass.

  cell cleared when its center is within R of the segment

  Adaptive clearing passes cam-adaptive.js

  • PartCraft
  64-bit

• Engagement check

  Re-simulates the passes on a finer grid and reports the largest engagement angle, the equivalent cutting width, uncut area and the smallest wall clearance.

  angle = 360 × (rim points in material) ÷ 360; width = R (1 − cos angle); gouge = min(dist to walls − R − leave)

  Adaptive clearing passes cam-adaptive.js

  • PartCraft
  64-bit

• Height grid of the part

  Samples the part's top surface on a grid for the first search of the tool-tip height.

  H[i, j] = height at cell center; cell = max(0.02, R ÷ 8)

  3D finishing toolpaths cam-finish.js

  • PartCraft
  32-bit in part

• Tool-tip height

  The lowest height at which the tool at (x, y) touches the part without cutting into it.

  z = max(H − h(ρ)) over grid samples within R; refine at ρ* = A + r_c s ÷ √(1 + s²) uphill; then max over triangle edges by ternary search; result = max(z + leave, floor)

  3D finishing toolpaths cam-finish.js

  • PartCraft
  32-bit in part

• Slope filter

  Whether the surface under a point is within the slope range chosen for the operation.

  s = √(g_x² + g_y²); tan(from) − 1e-9 ≤ s ≤ tan(to) + 1e-9

  3D finishing toolpaths cam-finish.js

  • PartCraft
  32-bit in part

• Finishing one straight line

  The 3D points of a straight pass over the part, dense enough to stay within the tolerance.

  split a span while |z(mid) − (z₀ + z₁) ÷ 2| > tol ÷ 2

  3D finishing toolpaths cam-finish.js

  • PartCraft
  64-bit

• Thinning a pass

  Drops points that lie on a straight run between their neighbors.

  drop p when its distance to the line through the last kept point and the next point ≤ tol ÷ 10

  3D finishing toolpaths cam-finish.js

  • PartCraft
  64-bit

• Parallel pass lines

  The positions of the raster lines across the part at the chosen angle.

  n = ceil((v₁ − v₀) ÷ (stepover × d) − 1e-9); line k at v₀ + (v₁ − v₀) k ÷ n

  3D finishing toolpaths cam-finish.js

  • PartCraft
  64-bit

• Cusp height

  The height of the ridge left between two ball passes a given distance apart on a flat surface.

  h = R − √(R² − (s ÷ 2)²)

  3D finishing toolpaths cam-finish.js

  • PartCraft
  64-bit

• Pass spacing for a cusp height

  The distance between passes that leaves ridges of a given height.

  s = 2 √(2 R h − h²); s = 2 R when h ≥ R

  3D finishing toolpaths cam-finish.js

  • PartCraft
  64-bit

• Distance over the surface

  The distance along the part's top surface from the starting cells to every other cell.

  shortest path over grid steps; step length = √((di × c)² + (dj × c)² + ΔH²)

  3D finishing toolpaths cam-finish.js

  • PartCraft
  64-bit

• Step directions of the distance search

  The set of grid steps the surface-distance search may take.

  all (di, dj) with |di|, |dj| ≤ 5 and no common factor

  3D finishing toolpaths cam-finish.js

  • PartCraft
  Exact

• Lines of equal surface distance

  Traces the lines at a given surface distance, which become the scallop passes.

  crossing on a cell edge at f = (level − a) ÷ (b − a)

  3D finishing toolpaths cam-finish.js

  • PartCraft
  64-bit

• Scallop spacing and levels

  The spacing of scallop passes from the cusp height, and the surface distances they are placed at.

  R_b = ball or corner radius + leave; s = spacing(R_b, cusp); level k = (k + ½) s; grid cell = max(0.02, min(s ÷ 3, d ÷ 8))

  3D finishing toolpaths cam-finish.js

  • PartCraft
  64-bit

• Simplifying a scallop pass

  Reduces the points of a 3D pass while staying within a quarter of the tolerance.

  keep the point farthest from the chord when its distance > tolerance ÷ 4, then repeat on both halves

  3D finishing toolpaths cam-finish.js

  • PartCraft
  64-bit

• Tool grown by the stock to leave

  Models stock to leave by making the cutter larger.

  d′ = d + 2 × leave; corner radius′ = corner radius + leave (bull nose)

  3D finishing toolpaths cam-finish.js

  • PartCraft
  64-bit

• Simulation grid

  Sets the cell size of the stock grid and the tolerances used to call a gouge.

  cell = min(2, max(0.1, max(w, h) ÷ 500)); lateral tolerance = 2e-4 × diagonal + 0.01

  Stock simulation and machining time cam-sim.js

  • PartCraft
  64-bit

• Cutting along a level move

  Lowers the stock cells under one level move of the tool.

  z_cell = min(z_cell, z + h(distance from cell center to the track))

  Stock simulation and machining time cam-sim.js

  • PartCraft
  64-bit

• Cutting along a sloping move

  Cuts a move that changes height as a series of short level moves.

  n = ceil(|Δz| ÷ 0.01); piece i cut at the lower of its two end heights

  Stock simulation and machining time cam-sim.js

  • PartCraft
  64-bit

• Stock volume

  The volume of stock left, from which the volume removed by each operation is found.

  V = cell² × Σ (z − stock bottom) over cells in the stock

  Stock simulation and machining time cam-sim.js

  • PartCraft
  64-bit

• Part height with lateral tolerance

  The part's height at a cell, taken as the lowest of the center and eight points a small distance round it.

  min over the center and 8 points at the lateral tolerance, 45° apart

  Stock simulation and machining time cam-sim.js

  • PartCraft
  64-bit

• Gouge detection

  Finds cells where the stock was cut below the part's surface.

  gouge when z_cell < eroded part height − 0.02

  Stock simulation and machining time cam-sim.js

  • PartCraft
  64-bit

• Stock left and deepest gouge

  The volume of stock left above the part, the thickest stock left and the deepest gouge.

  remaining = cell² × Σ (z − max(part height, stock bottom)) where that exceeds 0.02

  Stock simulation and machining time cam-sim.js

  • PartCraft
  64-bit