{
  "$schema": "https://slfy.solidify.studio/schema/slfy-0.1.schema.json",
  "format": "slfy",
  "version": "0.1",
  "model": {
    "id": "worm-reducer",
    "title": "Worm & Worm Wheel Reducer (30:1)",
    "summary": "A high-ratio, right-angle speed reducer featuring a single-start steel worm driving a 30-tooth bronze worm gear with self-locking capability.",
    "units": "mm",
    "parameters": [
      {
        "id": "z1",
        "label": "Worm starts (threads)",
        "symbol": "z_1",
        "value": 1,
        "min": 1,
        "max": 2,
        "step": 1,
        "unit": ""
      },
      {
        "id": "z2",
        "label": "Wheel teeth",
        "symbol": "z_2",
        "value": 30,
        "min": 20,
        "max": 60,
        "step": 1,
        "unit": ""
      },
      {
        "id": "m",
        "label": "Module",
        "symbol": "m",
        "value": 4,
        "min": 2,
        "max": 6,
        "step": 0.5,
        "unit": "mm"
      },
      {
        "id": "q",
        "label": "Diametral quotient",
        "symbol": "q",
        "value": 10,
        "min": 8,
        "max": 14,
        "step": 1,
        "unit": ""
      },
      {
        "id": "n_in",
        "label": "Input speed",
        "symbol": "n_{in}",
        "value": 1500,
        "min": 300,
        "max": 3000,
        "step": 50,
        "unit": "rpm"
      },
      {
        "id": "P_in",
        "label": "Input power",
        "symbol": "P_{in}",
        "value": 1.5,
        "min": 0.5,
        "max": 5,
        "step": 0.1,
        "unit": "kW"
      }
    ],
    "parts": [
      {
        "id": "gearbox_housing",
        "name": "Gearbox housing",
        "material": "castIron",
        "role": "housing",
        "position": [
          0,
          -0.02,
          0
        ],
        "explode": [
          0,
          -0.12,
          0
        ],
        "cut": true,
        "info": {
          "summary": "Ribbed cast iron casing and oil sump",
          "role": "Encloses the gearing, holds lubricating oil, and supports bearing bores for perpendicular shafts."
        },
        "shapes": [
          {
            "kind": "box",
            "position": [
              0,
              0,
              0
            ],
            "sx": 0.28,
            "sy": 0.22,
            "sz": 0.22
          },
          {
            "kind": "box",
            "op": "subtract",
            "position": [
              0,
              0.02,
              0
            ],
            "sx": 0.24,
            "sy": 0.18,
            "sz": 0.18
          },
          {
            "kind": "cylinder",
            "op": "subtract",
            "position": [
              0,
              -0.06,
              0
            ],
            "rotation": [
              0,
              0,
              1.5708
            ],
            "r": 0.032,
            "h": 0.3
          },
          {
            "kind": "cylinder",
            "op": "subtract",
            "position": [
              0,
              0.04,
              0
            ],
            "rotation": [
              1.5708,
              0,
              0
            ],
            "r": 0.035,
            "h": 0.24
          },
          {
            "kind": "box",
            "position": [
              0,
              -0.11,
              0
            ],
            "sx": 0.32,
            "sy": 0.02,
            "sz": 0.26
          }
        ]
      },
      {
        "id": "worm_shaft",
        "name": "Worm shaft",
        "material": "steel",
        "role": "moving",
        "rotation": [
          0,
          0,
          1.5708
        ],
        "explode": [
          -0.15,
          0,
          0
        ],
        "cut": false,
        "info": {
          "summary": "Case-hardened steel drive shaft with integral worm",
          "role": "Transmits high-speed input torque and drives the worm wheel through helical sliding mesh."
        },
        "motion": {
          "kind": "rotate",
          "axis": "y",
          "speed": "n_in / 60"
        },
        "mount": {
          "kind": "against",
          "target": "gearbox_housing",
          "face": "+y",
          "shift": [
            0,
            -0.15,
            0
          ]
        },
        "shapes": [
          {
            "kind": "cylinder",
            "r": 0.015,
            "h": 0.34
          },
          {
            "kind": "cylinder",
            "r": "(q * m / 2000)",
            "h": 0.1
          },
          {
            "kind": "cylinder",
            "r": "(q * m / 2000) + (m / 1000)",
            "h": 0.08
          },
          {
            "kind": "cylinder",
            "position": [
              0,
              0.08,
              0
            ],
            "r": 0.022,
            "h": 0.02
          },
          {
            "kind": "cylinder",
            "position": [
              0,
              -0.08,
              0
            ],
            "r": 0.022,
            "h": 0.02
          }
        ]
      },
      {
        "id": "worm_gear",
        "name": "Bronze worm wheel",
        "material": "bronze",
        "role": "moving",
        "rotation": [
          1.5708,
          0,
          0
        ],
        "explode": [
          0,
          0,
          0.14
        ],
        "cut": false,
        "info": {
          "summary": "Phosphor-bronze toothed rim bolted to hub",
          "role": "Meshes with the steel worm to provide low friction, high reduction ratio, and smooth torque transmission."
        },
        "motion": {
          "kind": "rotate",
          "axis": "y",
          "speed": "(n_in / 60) / (z2 / z1)"
        },
        "mount": {
          "kind": "against",
          "target": "worm_shaft",
          "face": "+y",
          "shift": [
            0,
            0.1,
            0
          ]
        },
        "shapes": [
          {
            "kind": "gear",
            "rInner": 0.025,
            "h": 0.038,
            "teeth": "z2",
            "module": "m / 1000"
          },
          {
            "kind": "cylinder",
            "r": 0.035,
            "h": 0.048
          }
        ]
      },
      {
        "id": "output_shaft",
        "name": "Output shaft",
        "material": "steelMatte",
        "role": "moving",
        "explode": [
          0,
          0,
          -0.14
        ],
        "cut": false,
        "info": {
          "summary": "Heavy-duty steel cross shaft",
          "role": "Transmits high output torque delivered by the worm wheel to the driven machinery."
        },
        "motion": {
          "kind": "rotate",
          "axis": "y",
          "speed": "(n_in / 60) / (z2 / z1)"
        },
        "mount": {
          "kind": "coaxial",
          "target": "worm_gear",
          "at": 0.5
        },
        "shapes": [
          {
            "kind": "cylinder",
            "r": 0.022,
            "h": 0.28
          },
          {
            "kind": "cylinder",
            "r": 0.026,
            "h": 0.05
          }
        ]
      },
      {
        "id": "bearings_worm",
        "name": "Tapered roller bearings (worm)",
        "material": "bearing",
        "role": "housing",
        "explode": [
          -0.08,
          0,
          0
        ],
        "cut": false,
        "info": {
          "summary": "Angular contact / tapered roller bearing pair",
          "role": "Carries large axial thrust loads and radial forces generated by the worm screw action."
        },
        "mount": {
          "kind": "coaxial",
          "target": "worm_shaft",
          "at": 0.18
        },
        "shapes": [
          {
            "kind": "tube",
            "rOuter": 0.03,
            "rInner": 0.018,
            "h": 0.018
          },
          {
            "kind": "tube",
            "position": [
              0,
              0.21,
              0
            ],
            "rOuter": 0.03,
            "rInner": 0.018,
            "h": 0.018
          }
        ]
      },
      {
        "id": "bearings_wheel",
        "name": "Radial ball bearings (wheel)",
        "material": "bearing",
        "role": "housing",
        "explode": [
          0,
          0,
          0.08
        ],
        "cut": false,
        "info": {
          "summary": "Deep-groove ball bearing set",
          "role": "Locates the output shaft and absorbs radial reactions and moderate side thrust."
        },
        "mount": {
          "kind": "coaxial",
          "target": "output_shaft",
          "at": 0.18
        },
        "shapes": [
          {
            "kind": "tube",
            "rOuter": 0.034,
            "rInner": 0.022,
            "h": 0.018
          },
          {
            "kind": "tube",
            "position": [
              0,
              0.18,
              0
            ],
            "rOuter": 0.034,
            "rInner": 0.022,
            "h": 0.018
          }
        ]
      }
    ],
    "annotations": [
      {
        "id": "in_torque",
        "kind": "moment",
        "label": "T_in",
        "magnitude": "P_in * 1000 * 60 / (2 * pi * n_in)",
        "unit": "N·m",
        "anchor": {
          "part": "worm_shaft",
          "at": "start"
        }
      },
      {
        "id": "out_torque",
        "kind": "moment",
        "label": "T_out",
        "magnitude": "T_out",
        "unit": "N·m",
        "anchor": {
          "part": "output_shaft",
          "at": "end"
        }
      }
    ],
    "calculations": [
      {
        "id": "ratio",
        "label": "Gear ratio",
        "symbol": "i",
        "formula": "z2 / z1",
        "unit": ":1",
        "latex": "i = \\frac{z_2}{z_1}"
      },
      {
        "id": "n_out",
        "label": "Output speed",
        "symbol": "n_{out}",
        "formula": "n_in / (z2 / z1)",
        "unit": "rpm",
        "latex": "n_{out} = \\frac{n_{in}}{i}"
      },
      {
        "id": "gamma_deg",
        "label": "Lead angle",
        "symbol": "\\gamma",
        "formula": "atan(z1 / q) * 180 / pi",
        "unit": "°",
        "latex": "\\gamma = \\arctan\\left(\\frac{z_1}{q}\\right)"
      },
      {
        "id": "eta",
        "label": "Efficiency",
        "symbol": "\\eta",
        "formula": "tan(atan(z1 / q)) / tan(atan(z1 / q) + 0.08)",
        "unit": "",
        "latex": "\\eta \\approx \\frac{\\tan\\gamma}{\\tan(\\gamma + \\rho)}"
      },
      {
        "id": "T_out",
        "label": "Output torque",
        "symbol": "T_{out}",
        "formula": "(P_in * 1000 * 60 / (2 * pi * (n_in / (z2 / z1)))) * (tan(atan(z1 / q)) / tan(atan(z1 / q) + 0.08))",
        "unit": "N·m",
        "latex": "T_{out} = \\frac{P_{in}\\eta}{\\omega_{out}}"
      }
    ],
    "charts": [
      {
        "id": "efficiency_curve",
        "title": "Efficiency vs Lead Angle",
        "x": {
          "label": "Lead angle",
          "unit": "°",
          "from": "2",
          "to": "40"
        },
        "y": {
          "label": "Efficiency",
          "unit": "%"
        },
        "series": [
          {
            "id": "eta_series",
            "label": "η (%)",
            "formula": "100 * tan(x * pi / 180) / tan((x + 4.5) * pi / 180)"
          }
        ]
      }
    ]
  },
  "view": {
    "camera": {
      "position": [
        0.42,
        0.32,
        0.48
      ],
      "target": [
        0,
        0,
        0
      ]
    },
    "extent": 0.45,
    "floorY": -0.18,
    "cut": {
      "enabled": true,
      "normal": [
        0,
        0,
        1
      ],
      "pos": 0.02
    }
  },
  "meta": {
    "generator": "Solidify (solidify.studio)",
    "license": "CC-BY-4.0",
    "created": "2026-11-10"
  }
}