Calculations

Calculations

• Buckling factors by subspace iteration

  The lowest positive buckling load factors and their mode shapes.

  Z = K⁻¹ G X; reduce (Zᵀ G Z, Zᵀ K Z); Kr = L Lᵀ; eig(L⁻¹ Gr L⁻ᵀ) = μ; λ = 1 ÷ μ

  Buckling load factors and thermal stress setup buckling.js

  • PartCraft
  64-bit

• Solver tolerances of a buckling study

  How tightly the pre-stress solve and each inner solve are converged.

  pre-stress: 1e-10; each K⁻¹ solve: 1e-9

  Buckling load factors and thermal stress setup buckling.js

  • PartCraft
  64-bit

• Temperature rise at each node

  The temperature change that drives thermal stress: a uniform rise, or the temperature field minus the stress-free temperature.

  ΔT = T − T_ref, T_ref = 20 when not given

  Buckling load factors and thermal stress setup buckling.js

  • PartCraft
  64-bit

• Time step for a transient thermal load

  Which saved time step of a transient run is nearest the requested time.

  step = round(time ÷ (t ÷ steps)), held in [0, steps]; time = step × dt

  Buckling load factors and thermal stress setup buckling.js

  • PartCraft
  64-bit

• Voxel model volume and mass

  The volume and mass of the analysis model listed with the study.

  volume = elements × h³; mass = volume × density (tonne/mm³) × 1000

  Buckling load factors and thermal stress setup buckling.js

  • PartCraft
  64-bit

• Numbers written to the deck

  Formats every coordinate, material value, load and penalty for the input deck.

  text = v.toExponential(10)

  CalculiX deck export and result import calculix.js

  • PartCraft
  64-bit

• Material cards

  Writes elastic constants, density and the two-point plastic curve of each part's material.

  density (tonne/mm³) = density (kg/m³) × 1e-12; plastic: (σ_y, 0) and (σ_y + H, 1)

  CalculiX deck export and result import calculix.js

  • PartCraft
  64-bit

• Support directions

  Writes each held direction, and a local axis system for supports on slanted faces.

  axis when ||v| − 1| < 1e-9; slanted: local x = n, local y = unit(t − (t · n) n)

  CalculiX deck export and result import calculix.js

  • PartCraft
  64-bit

• Nodal loads

  Writes the nodal forces of the study as concentrated loads.

  one line per non-zero force component

  CalculiX deck export and result import calculix.js

  • PartCraft
  64-bit

• Load increments

  The first and smallest load increment given to the other program.

  first = 1 ÷ steps; smallest = 1 ÷ (64 × steps); total and largest = 1

  CalculiX deck export and result import calculix.js

  • PartCraft
  64-bit

• Reading the result file

  Reads node positions and result values from the text result file.

  value = parseFloat(12-character field, D exponent read as E)

  CalculiX deck export and result import calculix.js

  • PartCraft
  64-bit

• Default penalty stiffness

  The contact stiffness used when none is given.

  kn = 20 × E ÷ h

  Contact between parts in stress analysis contact.js

  • PartCraft
  64-bit

• Closest point on a triangle

  The point of a flat triangle nearest a given point, as weights of the three corners.

  region tests on d₁ … d₆ = dot products of edges with corner-to-point vectors; inside: v = v_b ÷ (v_a + v_b + v_c)

  Contact between parts in stress analysis contact.js

  • PartCraft
  64-bit

• Closest point on a curved face

  The nearest point of a six-node master face, in the face's own coordinates.

  best of 4 flat sub-triangles (corners and midsides); (L₁, L₂) = weights × reference coordinates

  Contact between parts in stress analysis contact.js

  • PartCraft
  64-bit

• Point and normal on a face

  The position and outward unit normal of a six-node face at given face coordinates.

  x = Σ N_k x_k; n = unit(Σ ∂N_k/∂L₁ x_k × Σ ∂N_k/∂L₂ x_k)

  Contact between parts in stress analysis contact.js

  • PartCraft
  64-bit

• Integration weights on the slave face

  The area each contact point on a slave face stands for.

  w = w_q × |∂x/∂L₁ × ∂x/∂L₂| ÷ 2

  Contact between parts in stress analysis contact.js

  • PartCraft
  64-bit

• Pairing slave points with the master

  Finds the master point each slave point faces, and reports whether the pairing changed.

  paired when d² ≤ cutoff²; moved when the face changes or |ΔL| > 2e-3

  Contact between parts in stress analysis contact.js

  • PartCraft
  64-bit

• Gap, contact force and stiffness

  The normal gap at a contact point and the force and stiffness it adds.

  g = n · (x_s − x_m); force = kn × w × (−g) when g < 0; stiffness = kn × w × c cᵀ ⊗ n nᵀ; pressure = force ÷ w

  Contact between parts in stress analysis contact.js

  • PartCraft
  64-bit

• Bonded tie

  Holds a slave point to the master point it started nearest to.

  rel = (x_s − x_m) − (x_s − x_m) at the first call; force = −kt × w × rel

  Contact between parts in stress analysis contact.js

  • PartCraft
  64-bit

• Machined part: stock, cutting, holes, handling

  The cost rows of a part cut from a block of stock.

  stock = (size + 2 × allowance) per axis; stock cost = stock volume × density × 1e-9 × price per kg; cutting minutes = (stock volume − volume) ÷ removal rate × finishing; cost = minutes ÷ 60 × rate per hour

  Manufacturing cost estimate cost.js

  • PartCraft
  64-bit

• Printed part: filament and machine time

  The cost rows of a 3D-printed part.

  printed volume = volume × fill; filament = printed volume × density × 1e-9 × price per kg; hours = printed volume ÷ volume per hour

  Manufacturing cost estimate cost.js

  • PartCraft
  64-bit

• Cost per part and rounding

  The cost of each part at the given quantity, the share of each row, and the rounded figures returned.

  total = unit + setup ÷ quantity; share = row ÷ total; returned amounts = round to 0.01

  Manufacturing cost estimate cost.js

  • PartCraft
  64-bit

• Rounding to two decimals

  Rounds an amount or a listed quantity to hundredths.

  r2(v) = round(v × 100) ÷ 100

  Manufacturing cost estimate cost.js

  • PartCraft
  64-bit

• Number of holes

  Counts the holes the part has, for the time per hole.

  hole features + circles in cut sketches, each × (pattern count − 1) more for patterns

  Manufacturing cost estimate cost.js

  • PartCraft
  Exact

• 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

• 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

• Machining time

  The time a program takes: cutting moves at their feed, rapid moves at the machine's rapid rate, plus tool changes.

  seconds = 60 × (Σ L ÷ feed + Σ L ÷ rapid) + changes × change time

  Stock simulation and machining time cam-sim.js

  • PartCraft
  64-bit

• Arc center words I and J

  The arc center written relative to the arc's start point.

  I = round₃(c_x − round₃(start_x)); J = round₃(c_y − round₃(start_y))

  G-code and toolpath exports cam-post.js

  • PartCraft
  64-bit

• Axis words

  Writes X, Y and Z only when they change at the output resolution.

  write an axis when round₃(new) ≠ round₃(last written)

  G-code and toolpath exports cam-post.js

  • PartCraft
  64-bit

• Toolpath as CSV

  Writes every segment's start, end, arc center, sweep and feed as text.

  value = toFixed(6); sweep in degrees = sweep × 180 ÷ π

  G-code and toolpath exports cam-post.js

  • PartCraft
  64-bit

• Toolpath as JSON

  Writes the setup, tools and every operation's moves.

  JSON.stringify of the moves

  G-code and toolpath exports cam-post.js

  • PartCraft
  64-bit

• Spindle speed and feeds

  The spindle speed, cutting feed, plunge feed and ramp feed for a tool.

  rpm = round(1000 vc ÷ (π d)), limited to the machine's range; feed = rpm × flutes × f_z; plunge = feed ÷ 3; ramp = feed ÷ 2

  Cutting speeds, feeds and tool profiles cam-tools.js

  • PartCraft
  64-bit

• Rounding feeds to one decimal

  Rounds a feed rate to tenths.

  round1(v) = round(v × 10) ÷ 10

  Cutting speeds, feeds and tool profiles cam-tools.js

  • PartCraft
  64-bit

• Tool tip profile

  The height of the cutting surface above the tool's tip at a given distance from its axis.

  ball: R − √(R² − ρ²); bull: r_c − √(r_c² − (ρ − a)²) beyond a = R − r_c; drill and chamfer: (ρ − r_t) ÷ tan(angle ÷ 2); flat: 0

  Cutting speeds, feeds and tool profiles cam-tools.js

  • PartCraft
  64-bit

• Elementary functions

  The one-argument math functions a script can call: roots, exponentials, logarithms, trigonometry, hyperbolic functions, rounding and angle conversion.

  log1p(x) = x − x² ÷ 2 + x³ ÷ 3 for |x| < 1e-4, else log(1 + x); asinh(x) = sign × log(|x| + √(x² + 1)); atanh(x) = ½ log((1 + x) ÷ (1 − x)); sind(x) = sin(x × π ÷ 180)

  CraftScript core math functions cs-lib-core.js

  • PartCraft
  64-bit

• Rounding to a number of decimals

  round(x, d): rounds to d decimal places.

  round(x × 10^d) ÷ 10^d

  CraftScript core math functions cs-lib-core.js

  • PartCraft
  64-bit