Calculations

Calculations

• Revolve axis checks

  Checks that the axis lies in the sketch plane and that the profile stays on one side of it.

  side s = −u_y (p_x − a_x) + u_x (p_y − a_y); crosses when some s > 1e-7 × scale and some s < −1e-7 × scale

  Exact-kernel feature dimensions brep.js

  • PartCraft
  64-bit

• Revolve angle

  The sweep angle given to the kernel.

  full turn when |angle − 360| < 1e-9; else angle × π ÷ 180

  Exact-kernel feature dimensions brep.js

  • PartCraft
  64-bit

• Through-hole depth

  How deep a through hole is drilled.

  depth = distance to the body's far side + 1 + 0.01 × body range

  Exact-kernel feature dimensions brep.js

  • PartCraft
  64-bit

• Countersink depth

  How deep the cone of a countersunk hole goes.

  h = (D_csink − d) ÷ 2 ÷ tan(angle × π ÷ 360)

  Exact-kernel feature dimensions brep.js

  • PartCraft
  64-bit

• Cosmetic thread radii

  The major and minor radius recorded for a tapped hole's thread.

  r₁ = D ÷ 2; r₀ = min(tap drill, D − 1.082532 × P) ÷ 2

  Exact-kernel feature dimensions brep.js

  • PartCraft
  64-bit

• Linear pattern positions

  Where each copy of a linear pattern sits.

  copy i moved by direction × spacing × i

  Exact-kernel feature dimensions brep.js

  • PartCraft
  64-bit

• Circular pattern angles

  The angle of each copy of a circular pattern.

  full circle: step = 360 ÷ count; otherwise step = angle ÷ (count − 1); copy i turned by step × i

  Exact-kernel feature dimensions brep.js

  • PartCraft
  64-bit

• Shell wall offset

  Hollows a body to a wall thickness.

  offset = +t (outward) or −t; kernel tolerance 1e-3

  Exact-kernel feature dimensions brep.js

  • PartCraft
  64-bit

• Fillet and chamfer sizes

  The radius, distances or distance and angle given to the kernel for each picked edge.

  two distances: (d, d₂); distance and angle: (d, angle × π ÷ 180); fillet: r, or (r, r₂) along the edge

  Exact-kernel feature dimensions brep.js

  • PartCraft
  64-bit

• Sewing an imported surface model

  Joins the faces of a STEP file that has no solid into a closed shell.

  sewing tolerance = 1e-6

  Exact-kernel feature dimensions brep.js

  • PartCraft
  64-bit

• Mesh tolerances

  How closely the triangle mesh follows the exact faces.

  linear = 2e-4 × bounding-box diagonal; angular = 2π ÷ max(16, resolution)

  Exact solid: mesh, volume, area and tables brep.js

  • PartCraft
  64-bit

• Mesh read from the kernel

  Copies the mesh's vertices, normals and triangles out of the kernel's memory.

  vertices and normals: Float32Array view of the WebAssembly buffer

  Exact solid: mesh, volume, area and tables brep.js

  • PartCraft
  32-bit in part

• Welding the mesh

  Merges vertices that different faces share so the mesh is watertight.

  same vertex when x, y and z are identical

  Exact solid: mesh, volume, area and tables brep.js

  • PartCraft
  32-bit in part

• Volume and surface area

  The solid's volume and total surface area, from the exact faces.

  V = ∭ dV (Gauss–Kronrod, tolerance 1e-12, when a non-line, non-circle edge exists); A = ∬ dA

  Exact solid: mesh, volume, area and tables brep.js

  • PartCraft
  64-bit

• Genus

  The number of through holes (handles) of the solid, from the welded mesh.

  χ = V − E + F; genus = round(bodies − χ ÷ 2)

  Exact solid: mesh, volume, area and tables brep.js

  • PartCraft
  64-bit

• Face area and center

  Each face's area and center point, listed with the face.

  area = ∬ dA over the face; center = its centroid

  Exact solid: mesh, volume, area and tables brep.js

  • PartCraft
  64-bit

• Edge length and points

  Each edge's length, end points and middle point.

  length = ∫ |C′(t)| dt; middle = C((t₀ + t₁) ÷ 2)

  Exact solid: mesh, volume, area and tables brep.js

  • PartCraft
  64-bit

• Bounding box

  The smallest axis-aligned box around a shape.

  min, max per axis from the kernel's optimal box

  Exact solid: mesh, volume, area and tables brep.js

  • PartCraft
  64-bit

• Facts about an imported STEP file

  The solid count, face count, volume and bounding box shown when a STEP file is imported.

  volume = ∭ dV (default integration)

  Exact solid: mesh, volume, area and tables brep.js

  • PartCraft
  64-bit

• Stress at the integration points

  The six stress components at every integration point of every element, from the displacements.

  σ = D (ε − α ΔT I) per point, by the element's own routine

  Buckling load factors and thermal stress setup buckling.js

  • PartCraft
  64-bit

• Geometric stiffness times a vector

  Applies the stress-dependent stiffness Kσ to a vector, element by element.

  y = s × Σ_elements G_e x_e on each of the three directions

  Buckling load factors and thermal stress setup buckling.js

  • PartCraft
  64-bit

• 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

• Stock block

  The size and position of the stock around the part.

  offset mode: min = box min − (side, side, bottom), max = box max + (side, side, top); cylinder: r = ½ × box diagonal in XY + side

  Part and stock in machine coordinates cam.js

  • PartCraft
  64-bit

• Work origin and frame change

  Moves points from model coordinates to the work frame (G54) and back.

  work = (p · x, p · y, p · z) − origin

  Part and stock in machine coordinates cam.js

  • PartCraft
  64-bit

• Mesh in the work frame and snap tolerance

  Copies the part's mesh into work coordinates and sets how close a mesh point must be to an exact edge to be taken as that edge.

  tol = 1e-4 + 2e-6 × largest model dimension

  Part and stock in machine coordinates cam.js

  • PartCraft
  32-bit in part

• Where a vertical line meets the part

  The heights at which a vertical line through (x, y) crosses the part's surface.

  weights l₁, l₂, l₃ from the triangle's XY corners; z = l₁ z₁ + l₂ z₂ + l₃ z₃

  Part and stock in machine coordinates cam.js

  • PartCraft
  32-bit in part

• Top facet and its slope

  The height and slope of the highest mesh triangle under a point, used by 3D finishing.

  g_x = ((z₂ − z₁)(y₃ − y₁) − (z₃ − z₁)(y₂ − y₁)) ÷ d₂; g_y likewise

  Part and stock in machine coordinates cam.js

  • PartCraft
  32-bit in part