{
  "$schema": "https://slfy.solidify.studio/schema/slfy-0.1.schema.json",
  "format": "slfy",
  "version": "0.1",
  "model": {
    "id": "helical-gear-pair",
    "title": "Helical Gear Pair on Parallel Shafts",
    "summary": "Single-stage parallel-shaft helical gear pair with 25-tooth pinion and 50-tooth gear showing pitch geometry, center distance, and axial thrust generation.",
    "units": "mm",
    "parameters": [
      {
        "id": "z1",
        "label": "Pinion teeth",
        "symbol": "z_1",
        "value": 25,
        "min": 15,
        "max": 35,
        "step": 1,
        "unit": ""
      },
      {
        "id": "z2",
        "label": "Wheel teeth",
        "symbol": "z_2",
        "value": 50,
        "min": 30,
        "max": 80,
        "step": 1,
        "unit": ""
      },
      {
        "id": "mn",
        "label": "Normal module",
        "symbol": "m_n",
        "value": 3,
        "min": 2,
        "max": 5,
        "step": 0.5,
        "unit": "mm"
      },
      {
        "id": "beta",
        "label": "Helix angle",
        "symbol": "\\beta",
        "value": 20,
        "min": 10,
        "max": 35,
        "step": 1,
        "unit": "deg"
      },
      {
        "id": "b",
        "label": "Face width",
        "symbol": "b",
        "value": 40,
        "min": 25,
        "max": 60,
        "step": 5,
        "unit": "mm"
      },
      {
        "id": "rpm1",
        "label": "Pinion speed",
        "symbol": "n_1",
        "value": 1200,
        "min": 300,
        "max": 3000,
        "step": 100,
        "unit": "rpm"
      },
      {
        "id": "power",
        "label": "Transmitted power",
        "symbol": "P",
        "value": 7.5,
        "min": 1,
        "max": 20,
        "step": 0.5,
        "unit": "kW"
      }
    ],
    "parts": [
      {
        "id": "mounting_base",
        "name": "Gearbox Base Plate",
        "material": "castIron",
        "role": "housing",
        "position": [
          0.06,
          -0.16,
          0
        ],
        "explode": [
          0,
          -0.08,
          0
        ],
        "cut": false,
        "info": {
          "summary": "Rigid cast iron base plate with bearing pedestals.",
          "role": "Maintains shaft center distance and supports bearing reaction loads."
        },
        "shapes": [
          {
            "kind": "box",
            "sx": 0.38,
            "sy": 0.024,
            "sz": 0.28
          },
          {
            "kind": "box",
            "position": [
              -0.06,
              0.06,
              0.09
            ],
            "sx": 0.04,
            "sy": 0.12,
            "sz": 0.04
          },
          {
            "kind": "box",
            "position": [
              -0.06,
              0.06,
              -0.09
            ],
            "sx": 0.04,
            "sy": 0.12,
            "sz": 0.04
          },
          {
            "kind": "box",
            "position": [
              0.18,
              0.06,
              0.09
            ],
            "sx": 0.04,
            "sy": 0.12,
            "sz": 0.04
          },
          {
            "kind": "box",
            "position": [
              0.18,
              0.06,
              -0.09
            ],
            "sx": 0.04,
            "sy": 0.12,
            "sz": 0.04
          }
        ]
      },
      {
        "id": "pinion_shaft",
        "name": "Input Shaft",
        "material": "steel",
        "role": "moving",
        "rotation": [
          1.5708,
          0,
          0
        ],
        "explode": [
          0,
          0,
          -0.12
        ],
        "cut": false,
        "info": {
          "summary": "High-strength alloy steel input drive shaft.",
          "role": "Transmits input torque and accommodates radial and axial bearing reactions."
        },
        "motion": {
          "kind": "rotate",
          "axis": "y",
          "speed": "rpm1 / 60"
        },
        "mount": {
          "kind": "against",
          "target": "mounting_base",
          "face": "+y",
          "shift": [
            -0.12,
            0.16,
            0
          ]
        },
        "shapes": [
          {
            "kind": "cylinder",
            "r": 0.014,
            "h": 0.24
          },
          {
            "kind": "cylinder",
            "r": 0.018,
            "h": 0.06
          }
        ]
      },
      {
        "id": "pinion",
        "name": "Helical Pinion (25T)",
        "material": "forged",
        "role": "moving",
        "explode": [
          0,
          0.08,
          0
        ],
        "cut": false,
        "info": {
          "summary": "Case-hardened 25-tooth right-hand helical pinion.",
          "role": "Drives the mating wheel with smooth progressive tooth engagement along the helix."
        },
        "motion": {
          "kind": "rotate",
          "axis": "y",
          "speed": "rpm1 / 60"
        },
        "mount": {
          "kind": "coaxial",
          "target": "pinion_shaft",
          "at": 0.5
        },
        "shapes": [
          {
            "kind": "gear",
            "rInner": 0.014,
            "h": "b * 0.001",
            "teeth": "z1",
            "module": "mt * 0.001",
            "helixAngle": "beta"
          }
        ]
      },
      {
        "id": "driven_gear",
        "name": "Helical Wheel (50T)",
        "material": "steelMatte",
        "role": "moving",
        "explode": [
          0,
          -0.08,
          0
        ],
        "cut": false,
        "info": {
          "summary": "50-tooth left-hand helical gear wheel.",
          "role": "Receives torque from the pinion at reduced speed and opposite axial thrust."
        },
        "motion": {
          "kind": "rotate",
          "axis": "y",
          "speed": "-rpm1 / (60 * u)"
        },
        "mount": {
          "kind": "mesh",
          "target": "pinion",
          "side": "+x"
        },
        "shapes": [
          {
            "kind": "gear",
            "rInner": 0.02,
            "h": "b * 0.001",
            "teeth": "z2",
            "module": "mt * 0.001",
            "helixAngle": "-beta"
          },
          {
            "kind": "cylinder",
            "op": "subtract",
            "r": "0.0005 * d2 - 0.012",
            "h": "b * 0.001 * 0.4"
          }
        ]
      },
      {
        "id": "output_shaft",
        "name": "Output Shaft",
        "material": "steel",
        "role": "moving",
        "explode": [
          0,
          0,
          0.12
        ],
        "cut": false,
        "info": {
          "summary": "Heavy-duty parallel output shaft.",
          "role": "Delivers multiplied torque to the load system."
        },
        "motion": {
          "kind": "rotate",
          "axis": "y",
          "speed": "-rpm1 / (60 * u)"
        },
        "mount": {
          "kind": "coaxial",
          "target": "driven_gear",
          "at": 0.5
        },
        "shapes": [
          {
            "kind": "cylinder",
            "r": 0.02,
            "h": 0.24
          },
          {
            "kind": "cylinder",
            "r": 0.024,
            "h": "b * 0.001 + 0.01"
          }
        ]
      },
      {
        "id": "bearings",
        "name": "Tapered Roller Bearings",
        "material": "bearing",
        "role": "static",
        "explode": [
          0,
          0,
          -0.06
        ],
        "cut": false,
        "info": {
          "summary": "Angular contact / tapered roller bearing pairs.",
          "role": "Reacts combined radial loads and axial thrust induced by helical teeth."
        },
        "mount": {
          "kind": "coaxial",
          "target": "pinion_shaft",
          "at": 0.15
        },
        "shapes": [
          {
            "kind": "tube",
            "rOuter": 0.028,
            "rInner": 0.014,
            "h": 0.022
          },
          {
            "kind": "tube",
            "position": [
              0,
              0.14,
              0
            ],
            "rOuter": 0.028,
            "rInner": 0.014,
            "h": 0.022
          }
        ]
      }
    ],
    "annotations": [
      {
        "id": "ann_torque",
        "kind": "moment",
        "label": "T_1",
        "magnitude": "T1",
        "unit": "N·m",
        "anchor": {
          "part": "pinion_shaft",
          "at": "start"
        }
      },
      {
        "id": "ann_thrust",
        "kind": "force",
        "label": "F_a",
        "magnitude": "Fa",
        "unit": "N",
        "anchor": {
          "part": "pinion",
          "at": "+x"
        },
        "direction": "+y",
        "length": 0.1
      },
      {
        "id": "ann_tangential",
        "kind": "force",
        "label": "F_t",
        "magnitude": "Ft",
        "unit": "N",
        "anchor": {
          "part": "pinion",
          "at": "+x"
        },
        "direction": "+z",
        "length": 0.12
      }
    ],
    "calculations": [
      {
        "id": "u",
        "label": "Gear ratio",
        "symbol": "u",
        "formula": "z2 / z1",
        "unit": "",
        "latex": "u = \\frac{z_2}{z_1}"
      },
      {
        "id": "mt",
        "label": "Transverse module",
        "symbol": "m_t",
        "formula": "mn / cos(beta * pi / 180)",
        "unit": "mm",
        "latex": "m_t = \\frac{m_n}{\\cos\\beta}"
      },
      {
        "id": "d1",
        "label": "Pinion pitch diameter",
        "symbol": "d_1",
        "formula": "z1 * mt",
        "unit": "mm",
        "latex": "d_1 = z_1 m_t"
      },
      {
        "id": "d2",
        "label": "Wheel pitch diameter",
        "symbol": "d_2",
        "formula": "z2 * mt",
        "unit": "mm",
        "latex": "d_2 = z_2 m_t"
      },
      {
        "id": "a",
        "label": "Center distance",
        "symbol": "a",
        "formula": "(d1 + d2) / 2",
        "unit": "mm",
        "latex": "a = \\frac{d_1 + d_2}{2}"
      },
      {
        "id": "T1",
        "label": "Pinion torque",
        "symbol": "T_1",
        "formula": "power * 1000 / (2 * pi * rpm1 / 60)",
        "unit": "N·m",
        "latex": "T_1 = \\frac{P}{\\omega_1}"
      },
      {
        "id": "Ft",
        "label": "Tangential tooth force",
        "symbol": "F_t",
        "formula": "2000 * T1 / d1",
        "unit": "N",
        "latex": "F_t = \\frac{2 T_1}{d_1}"
      },
      {
        "id": "Fa",
        "label": "Axial thrust force",
        "symbol": "F_a",
        "formula": "Ft * tan(beta * pi / 180)",
        "unit": "N",
        "latex": "F_a = F_t \\tan\\beta"
      }
    ],
    "charts": [
      {
        "id": "thrust_vs_beta",
        "title": "Axial Thrust Force vs Helix Angle",
        "x": {
          "label": "Helix angle β",
          "unit": "deg",
          "from": "10",
          "to": "35"
        },
        "y": {
          "label": "Thrust Force Fa",
          "unit": "N"
        },
        "series": [
          {
            "id": "fa_curve",
            "label": "Axial Force Fa(β)",
            "formula": "Ft * tan(x * pi / 180)"
          }
        ]
      }
    ]
  },
  "view": {
    "camera": {
      "position": [
        0.45,
        0.35,
        0.48
      ],
      "target": [
        0.06,
        0.02,
        0
      ]
    },
    "extent": 0.55,
    "floorY": -0.22,
    "cut": {
      "enabled": false,
      "normal": [
        0,
        0,
        1
      ],
      "pos": 0.01
    }
  },
  "meta": {
    "generator": "Solidify (solidify.studio)",
    "license": "CC-BY-4.0",
    "created": "2026-11-10"
  }
}