Calculations

Calculations

• Mean outward normal at picked nodes

  The direction used for pressure and normal force at each node of a picked face.

  n = Σ face normals ÷ |Σ face normals|

  Voxel grid of a part voxel.js

  • PartCraft
  32-bit in part

• Cubes near picked faces

  Marks the cubes whose centers are within a distance of picked faces, for preserve and obstacle regions.

  kept when the distance from the cube center to the faces' triangles ≤ dist

  Voxel grid of a part voxel.js

  • PartCraft
  64-bit

• Section outline at its anchor

  The section's outline moved so the chosen anchor point sits on the member's line, with its width, height and radius.

  w = u_max − u_min; h = v_max − v_min; R = max |point|

  Structural members and their cut list weldment.js

  • PartCraft
  64-bit

• Member orientation

  The across and depth directions of a member's section about its line.

  v = up − (up·d) d, normalized; u = v × d; then rotated about d

  Structural members and their cut list weldment.js

  • PartCraft
  64-bit

• When line ends meet

  The distance within which two line ends count as one joint.

  tol = 10⁻⁶ × max(1, largest |end point|, longest member)

  Structural members and their cut list weldment.js

  • PartCraft
  64-bit

• How far a member runs past a corner

  The extra length a raw member needs so a miter cut still has material.

  ext = min(50 R, R ÷ max(tan(angle ÷ 2), 0.02)) + R

  Structural members and their cut list weldment.js

  • PartCraft
  64-bit

• Miter cut plane

  The plane halfway between two members that both are cut on.

  n = (d_in + d_out) ÷ |d_in + d_out|; offset = n·P

  Structural members and their cut list weldment.js

  • PartCraft
  64-bit

• Butt cut planes

  Where the through member ends and where the other is cut square against it.

  reach = max |(u U + v V)·d| over the outline; offsets = ∓(d·P) ∓ reach

  Structural members and their cut list weldment.js

  • PartCraft
  64-bit

• Gusset plate

  The triangular plate in a corner and the angle listed for it.

  corners (0, 0), (s, 0), (s d_out·x, s d_out·y); angle = acos(x·d_out)

  Structural members and their cut list weldment.js

  • PartCraft
  64-bit

• Cut length and end angles of a member

  The length of each finished piece along its line and the angle of each end cut, as stored in the cut list.

  length = round((max s − min s) × 10) ÷ 10, s = (vertex − a)·d; angle = round(acos(|cut·d|) × 180 ÷ π × 100) ÷ 100

  Structural members and their cut list weldment.js

  • PartCraft
  32-bit in part

• Cut list rows

  Groups identical pieces and counts them.

  same piece when section, length to one decimal, both angles and both end kinds match

  Structural members and their cut list weldment.js

  • PartCraft
  32-bit in part

• Cut list CSV

  Writes the cut list as CSV text.

  member: length with one decimal; cap: w × h with one decimal

  Structural members and their cut list weldment.js

  • PartCraft
  32-bit in part

• Cage move from the gizmo

  The transform applied to the selected cage vertices while the gizmo is dragged.

  M = W_now × W_start⁻¹

  Freeform cage edits from the workspace ws-form.js

  • PartCraft
  64-bit

• Point for a new face

  The position stored when a face is drawn by clicks.

  existing vertex within 9 px, else ray ∩ plane y = 0 rounded to 0.001

  Freeform cage edits from the workspace ws-form.js

  • PartCraft
  64-bit

• Direction of an edge extrusion

  The direction and distance open edges are extruded by.

  d = Σ (edge middle − face center); offset = d ÷ |d| × distance

  Freeform cage edits from the workspace ws-form.js

  • PartCraft
  64-bit

• Tolerance for joining a new face

  The distance within which a new face's points join existing cage vertices.

  tol = 10⁻⁶ × max(1, size setting)

  Freeform cage edits from the workspace ws-form.js

  • PartCraft
  64-bit

• Picked point as an anchor

  The anchor position in the part's own axes and the face normal at the pick.

  p = M⁻¹ p_pick, each coordinate rounded to 6 decimals; n = (b − a) × (c − a) ÷ length

  Anchor points of manual annotations ws-illustrate.js

  • PartCraft
  64-bit

• Is a face square to the tool axis

  Decides whether a picked flat or round face can be machined from the setup's tool axis.

  accepted when ||n·axis| − 1| ≤ 10⁻⁹

  Machining picks and readouts ws-manufacture.js

  • PartCraft
  64-bit

• Matching a pick to one already stored

  Decides whether a clicked face is already in the operation's geometry, to add or remove it.

  same when names agree and |at − ref| < 10⁻³

  Machining picks and readouts ws-manufacture.js

  • PartCraft
  64-bit

• Numbers shown in the panel

  Formats stock sizes, feeds, gouge depth and remaining stock for the panel.

  text = value rounded to dp decimals (3 by default), trailing zeros dropped

  Machining picks and readouts ws-manufacture.js

  • PartCraft
  64-bit

• Part mesh for scripts

  The open part as a triangle mesh a script can compute on through part().

  Script workspace: the part handed to scripts and picked values ws-script.js

  • PartCraft
  32-bit in part

• Picked point and nearest node

  The coordinates of the clicked point and the mesh node closest to it.

  node = the hit triangle's corner with the least √(Δx² + Δy² + Δz²) to the hit point

  Script workspace: the part handed to scripts and picked values ws-script.js

  • PartCraft
  32-bit in part

• Field values at the picked node or element

  The value of each shown field at the picked node or element.

  Script workspace: the part handed to scripts and picked values ws-script.js

  • PartCraft
  64-bit

• Deformed shape for drawing

  The drawn position of each surface corner when a displacement field deforms the shape.

  drawn position = position + scale × displacement

  Script workspace: the part handed to scripts and picked values ws-script.js

  • PartCraft
  32-bit, display only

• Element size of a live analysis level

  The element size the coarse and refined live solves use.

  h = base size × level factor

  Simulation workspace: plot values and the hover probe ws-simulation.js

  • PartCraft
  64-bit

• Mode shape magnitude

  The size of the mode shape's displacement at each plot vertex.

  |u| = √(u_x² + u_y² + u_z²)

  Simulation workspace: plot values and the hover probe ws-simulation.js

  • PartCraft
  32-bit in part

• Safety factor plot values

  The safety factor at each plot vertex, for coloring.

  safety = min(yield ÷ stress, 100)

  Simulation workspace: plot values and the hover probe ws-simulation.js

  • PartCraft
  32-bit, display only

• Legend range

  The least and largest value of a plotted result, for the legend.

  Simulation workspace: plot values and the hover probe ws-simulation.js

  • PartCraft
  64-bit

• Result under the pointer

  The stress, displacement, strain and safety factor at the point under the pointer.

  value = w₀v₀ + w₁v₁ + w₂v₂; safety = yield ÷ stress

  Simulation workspace: plot values and the hover probe ws-simulation.js

  • PartCraft
  32-bit in part

• Barycentric weights

  The three weights of a point inside a triangle.

  w₁ = (d₁₁d₂₀ − d₀₁d₂₁) ÷ (d₀₀d₁₁ − d₀₁²); w₂ = (d₀₀d₂₁ − d₀₁d₂₀) ÷ (d₀₀d₁₁ − d₀₁²); w₀ = 1 − w₁ − w₂

  Simulation workspace: plot values and the hover probe ws-simulation.js

  • PartCraft
  64-bit

• Deformed plot positions

  The drawn position of each plot vertex when the deformed shape is shown.

  drawn position = position + scale × displacement

  Simulation workspace: plot values and the hover probe ws-simulation.js

  • PartCraft
  32-bit, display only

• Automatic deformation scale

  The factor the displacements are multiplied by so the deformed shape can be seen.

  raw = 0.08 × box diagonal ÷ largest |u|, rounded up to 1, 2, 5 or 10 × 10ᵉ

  Simulation workspace: plot values and the hover probe ws-simulation.js

  • PartCraft
  32-bit, display only

• Rounding to 3 decimals

  Rounds a number to a multiple of 0.001 before it is stored.

  round(v × 1000) ÷ 1000

  Add-on display bodies: stored coordinates and placement addons/addon-bodies.js

  • PartCraft
  64-bit

• Body coordinates as stored

  The box corners or mesh positions, offset and turn of one body as they go into the part file.

  Add-on display bodies: stored coordinates and placement addons/addon-bodies.js

  • PartCraft
  64-bit

• Body placed in the world

  Turns a body's points about the Y axis and moves them by its offset.

  x′ = x cos a + z sin a + t_x; y′ = y + t_y; z′ = −x sin a + z cos a + t_z; a = rotY × π ÷ 180

  Add-on display bodies: stored coordinates and placement addons/addon-bodies.js

  • PartCraft
  64-bit

• Box of all add-on bodies

  The least and largest coordinates of every placed add-on body.

  Add-on display bodies: stored coordinates and placement addons/addon-bodies.js

  • PartCraft
  64-bit

• Rounding for the panel

  Rounds a result to a few significant digits before the panel words it.

  Advanced simulation add-on: result summary and color bands addons/advanced-sim/lib/results.js

  • PartCraft
  64-bit

• Summary rows

  The load reached, largest displacement and stress, plastic strain, contact force and penetration of a result.

  load = √(F_x² + F_y² + F_z²) × λ; penetration % = 100 × penetration ÷ h

  Advanced simulation add-on: result summary and color bands addons/advanced-sim/lib/results.js

  • PartCraft
  64-bit

• Color bands and legend

  Splits the plot mesh into bands of equal value range and gives each band's limits.

  band = floor((v − lo) ÷ (hi − lo) × n), clamped to 0 … n − 1; limits: lo + (hi − lo) × i ÷ n

  Advanced simulation add-on: result summary and color bands addons/advanced-sim/lib/results.js

  • PartCraft
  64-bit

• A flat face's box in its own plane

  The extent of a flat face along two axes lying in its plane.

  u = (n × t) ÷ |n × t|; v = n × u; box = least and largest p·u and p·v over the face's triangle corners

  Advanced simulation add-on: finding contact pairs addons/advanced-sim/lib/setup.js

  • PartCraft
  32-bit in part

• Facing faces within a gap

  The pairs of flat faces that face each other, with their gap and overlap.

  n·m ≤ −cos 0.5°; d = (o_B − o_A)·n with −1e-6 ≤ d ≤ gap; overlap = w × h

  Advanced simulation add-on: finding contact pairs addons/advanced-sim/lib/setup.js

  • PartCraft
  64-bit

• Triangle areas and centroids

  The area and center of each mesh triangle.

  area = |(b − a) × (c − a)| ÷ 2; centroid = (a + b + c) ÷ 3 × 1000

  Magnetics add-on: field readout, flux lines and exports addons/magnetics/lib/results.js

  • PartCraft
  64-bit

• Area, mean and peak flux density of each body

  Each body's area in mm², its area-weighted mean |B| and its largest |B|.

  mean B = Σ(Bₑ × areaₑ) ÷ Σ areaₑ

  Magnetics add-on: field readout, flux lines and exports addons/magnetics/lib/results.js

  • PartCraft
  32-bit in part

• Result against a hand formula

  The value the result gives where a template's hand formula applies, and its relative difference.

  got = Σ(v × w) ÷ Σ w; diff = got ÷ want − 1

  Magnetics add-on: field readout, flux lines and exports addons/magnetics/lib/results.js

  • PartCraft
  32-bit in part

• Flux lines

  Contour segments of the vector potential A, and the flux between neighboring lines.

  levelᵢ = lo + ΔA × (i + 1), ΔA = (hi − lo) ÷ (k + 1); t = (L − aᵢ) ÷ (aⱼ − aᵢ)

  Magnetics add-on: field readout, flux lines and exports addons/magnetics/lib/results.js

  • PartCraft
  32-bit in part

• Top of the color scale

  The |B| that the top color stands for.

  Magnetics add-on: field readout, flux lines and exports addons/magnetics/lib/results.js

  • PartCraft
  32-bit, display only

• Number format of the exports

  How a number is written into the CSV and VTK files.

  Magnetics add-on: field readout, flux lines and exports addons/magnetics/lib/results.js

  • PartCraft
  64-bit

• Field table (CSV)

  One row per triangle: center, region, area and B.

  Magnetics add-on: field readout, flux lines and exports addons/magnetics/lib/results.js

  • PartCraft
  32-bit in part

• VTK file

  The mesh in mm with B per triangle and A per node.

  Magnetics add-on: field readout, flux lines and exports addons/magnetics/lib/results.js

  • PartCraft
  32-bit in part

• Summary table (CSV)

  Peak B, each body's area, mean and peak B, forces, torque and the hand-formula check.

  Magnetics add-on: field readout, flux lines and exports addons/magnetics/lib/results.js

  • PartCraft
  32-bit in part