{
  "title": "Endmill Deflection Calculator — data twin",
  "author": "Anna Brown",
  "site": "https://anna-brown.4ort.net/tool-deflection.html",
  "formula": {
    "deflection_in": "delta = F * L^3 / (3 * E * I)",
    "moment_of_inertia_round_shank_in4": "I = pi * d^4 / 64",
    "cantilever_stiffness_lbf_per_in": "k = 3 * E * I / L^3",
    "E_carbide_psi": 30000000,
    "E_hss_psi": 29500000,
    "E_cobalt_hss_psi": 22000000
  },
  "worked_example": {
    "material": "1018 steel slot, 0.75 in wide",
    "tool": "solid carbide endmill",
    "diameter_in": 0.375,
    "stickout_in": 2.0,
    "force_lbf": 180,
    "I_in4": 0.000969,
    "3EI_lbf_in2": 87200,
    "deflection_in": 0.0165,
    "thou": 16.5,
    "note": "at 1.25 in stickout same force: deflection 0.010 in; at 120 lbf: 0.0063 in"
  },
  "conversions": {
    "1_thou_in": 0.001,
    "in_to_mm": 25.4
  },
  "failure_modes": [
    "regenerative_chatter_is_dynamic_not_static",
    "force_spread_along_flute_not_point_load",
    "chuck_spindle_column_compliance_stacks_in_series",
    "necked_tools_have_nonuniform_I",
    "belt_drive_torsional_windup"
  ],
  "grounding": {
    "machining": "https://4ort.xyz/entity/machining",
    "wikidata_Q192047": "subtractive manufacturing by material removal"
  }
}