{
  "$schema": "https://slfy.solidify.studio/schema/slfy-0.1.schema.json",
  "format": "slfy",
  "version": "0.1",
  "model": {
    "id": "open-differential",
    "title": "Open Differential Mechanism",
    "summary": "An open differential gear train that splits input torque equally between two drive axles while allowing them to rotate at different speeds during cornering.",
    "units": "mm",
    "parameters": [
      {
        "id": "N_ring",
        "label": "Ring gear teeth",
        "symbol": "z_r",
        "value": 41,
        "min": 35,
        "max": 49,
        "step": 2,
        "unit": ""
      },
      {
        "id": "N_pinion",
        "label": "Drive pinion teeth",
        "symbol": "z_p",
        "value": 10,
        "min": 8,
        "max": 14,
        "step": 1,
        "unit": ""
      },
      {
        "id": "N_spider",
        "label": "Spider gear teeth",
        "symbol": "z_s",
        "value": 10,
        "min": 8,
        "max": 14,
        "step": 1,
        "unit": ""
      },
      {
        "id": "N_side",
        "label": "Side gear teeth",
        "symbol": "z_a",
        "value": 16,
        "min": 12,
        "max": 20,
        "step": 2,
        "unit": ""
      },
      {
        "id": "input_rpm",
        "label": "Carrier input speed",
        "symbol": "n_c",
        "value": 300,
        "min": 60,
        "max": 1200,
        "step": 30,
        "unit": "rpm"
      },
      {
        "id": "delta_rpm",
        "label": "Differential wheel split",
        "symbol": "Δn",
        "value": 60,
        "min": -150,
        "max": 150,
        "step": 10,
        "unit": "rpm"
      },
      {
        "id": "input_torque",
        "label": "Input ring torque",
        "symbol": "T_in",
        "value": 350,
        "min": 100,
        "max": 800,
        "step": 25,
        "unit": "N·m"
      }
    ],
    "parts": [
      {
        "id": "carrier",
        "name": "Differential Carrier Case",
        "material": "castIron",
        "role": "housing",
        "position": [
          0,
          0,
          0
        ],
        "rotation": [
          0,
          0,
          1.5708
        ],
        "explode": [
          0,
          0.12,
          0
        ],
        "cut": true,
        "info": {
          "summary": "Differential cage housing",
          "role": "Houses and supports the cross pin and side gears while rotating at the mean axle speed driven by the crown ring gear."
        },
        "motion": {
          "kind": "rotate",
          "axis": "x",
          "speed": "input_rpm / 60"
        },
        "shapes": [
          {
            "kind": "cylinder",
            "r": 0.082,
            "h": 0.11
          },
          {
            "kind": "cylinder",
            "op": "subtract",
            "r": 0.068,
            "h": 0.09
          },
          {
            "kind": "tube",
            "rOuter": 0.042,
            "rInner": 0.024,
            "h": 0.17
          },
          {
            "kind": "cylinder",
            "position": [
              0,
              -0.035,
              0
            ],
            "r": 0.098,
            "h": 0.012
          },
          {
            "kind": "cylinder",
            "op": "subtract",
            "rotation": [
              1.5708,
              0,
              0
            ],
            "r": 0.011,
            "h": 0.14
          }
        ]
      },
      {
        "id": "ring_gear",
        "name": "Crown Ring Gear",
        "material": "steel",
        "role": "moving",
        "explode": [
          -0.12,
          0,
          0
        ],
        "cut": false,
        "info": {
          "summary": "Crown bevel ring gear",
          "role": "Receives engine torque from the drive pinion shaft and transmits it directly into the revolving differential case."
        },
        "motion": {
          "kind": "rotate",
          "axis": "x",
          "speed": "input_rpm / 60"
        },
        "mount": {
          "kind": "coaxial",
          "target": "carrier",
          "at": 0.25,
          "offset": -0.01
        },
        "shapes": [
          {
            "kind": "gear",
            "rInner": 0.082,
            "h": 0.024,
            "teeth": "N_ring",
            "module": 0.0042
          },
          {
            "kind": "tube",
            "position": [
              0,
              -0.012,
              0
            ],
            "rOuter": 0.105,
            "rInner": 0.082,
            "h": 0.018
          },
          {
            "kind": "cylinder",
            "op": "subtract",
            "radialCount": 8,
            "radialRadius": 0.092,
            "r": 0.005,
            "h": 0.03
          }
        ]
      },
      {
        "id": "cross_pin",
        "name": "Spider Cross Pin",
        "material": "steelDark",
        "role": "moving",
        "rotation": [
          1.5708,
          0,
          0
        ],
        "explode": [
          0,
          0.15,
          0
        ],
        "cut": false,
        "info": {
          "summary": "Differential spider shaft",
          "role": "Mounts rigidly inside the revolving carrier to provide rotation axes for the two planetary spider pinion gears."
        },
        "motion": {
          "kind": "rotate",
          "axis": "x",
          "speed": "input_rpm / 60"
        },
        "mount": {
          "kind": "coaxial",
          "target": "carrier",
          "at": 0.5,
          "offset": 0
        },
        "shapes": [
          {
            "kind": "cylinder",
            "r": 0.01,
            "h": 0.132
          },
          {
            "kind": "cylinder",
            "op": "subtract",
            "position": [
              0,
              0.058,
              0
            ],
            "rotation": [
              0,
              0,
              1.5708
            ],
            "r": 0.002,
            "h": 0.022
          }
        ]
      },
      {
        "id": "spider_top",
        "name": "Upper Spider Pinion Gear",
        "material": "bronze",
        "role": "moving",
        "rotation": [
          0,
          3.1416,
          0
        ],
        "explode": [
          0,
          0.1,
          0
        ],
        "cut": false,
        "info": {
          "summary": "Top bevel spider gear",
          "role": "Transfers torque from the cross pin to both side gears, rotating on its pin only when the two drive wheels differ in speed."
        },
        "motion": {
          "kind": "rotate",
          "axis": "y",
          "speed": "spider_spin / 60"
        },
        "mount": {
          "kind": "coaxial",
          "target": "cross_pin",
          "at": 0.8,
          "offset": 0
        },
        "shapes": [
          {
            "kind": "bevelGear",
            "rInner": 0.0105,
            "h": 0.018,
            "teeth": "N_spider",
            "module": 0.0038
          },
          {
            "kind": "tube",
            "rOuter": 0.026,
            "rInner": 0.0105,
            "h": 0.01
          }
        ]
      },
      {
        "id": "spider_bottom",
        "name": "Lower Spider Pinion Gear",
        "material": "bronze",
        "role": "moving",
        "explode": [
          0,
          -0.1,
          0
        ],
        "cut": false,
        "info": {
          "summary": "Bottom bevel spider gear",
          "role": "Balances driving torque symmetrically across the opposing side gears together with the upper spider pinion."
        },
        "motion": {
          "kind": "rotate",
          "axis": "y",
          "speed": "-spider_spin / 60"
        },
        "mount": {
          "kind": "coaxial",
          "target": "cross_pin",
          "at": 0.2,
          "offset": 0
        },
        "shapes": [
          {
            "kind": "bevelGear",
            "rInner": 0.0105,
            "h": 0.018,
            "teeth": "N_spider",
            "module": 0.0038
          },
          {
            "kind": "tube",
            "rOuter": 0.026,
            "rInner": 0.0105,
            "h": 0.01
          }
        ]
      },
      {
        "id": "side_gear_left",
        "name": "Left Side Gear & Axle Stub",
        "material": "steel",
        "role": "moving",
        "rotation": [
          0,
          0,
          1.5708
        ],
        "explode": [
          -0.14,
          0,
          0
        ],
        "cut": false,
        "info": {
          "summary": "Left side bevel gear and half-shaft spline",
          "role": "Meshes with both spider pinions to deliver driving torque to the left wheel half-shaft."
        },
        "motion": {
          "kind": "rotate",
          "axis": "x",
          "speed": "n_left / 60"
        },
        "mount": {
          "kind": "coaxial",
          "target": "carrier",
          "at": 0.28,
          "offset": 0
        },
        "shapes": [
          {
            "kind": "bevelGear",
            "rInner": 0.014,
            "h": 0.02,
            "teeth": "N_side",
            "module": 0.0038
          },
          {
            "kind": "cylinder",
            "position": [
              0,
              0.05,
              0
            ],
            "r": 0.015,
            "h": 0.12
          },
          {
            "kind": "tube",
            "position": [
              0,
              0.008,
              0
            ],
            "rOuter": 0.028,
            "rInner": 0.015,
            "h": 0.015
          }
        ]
      },
      {
        "id": "side_gear_right",
        "name": "Right Side Gear & Axle Stub",
        "material": "steel",
        "role": "moving",
        "rotation": [
          0,
          0,
          -1.5708
        ],
        "explode": [
          0.14,
          0,
          0
        ],
        "cut": false,
        "info": {
          "summary": "Right side bevel gear and half-shaft spline",
          "role": "Meshes with both spider pinions to deliver driving torque to the right wheel half-shaft."
        },
        "motion": {
          "kind": "rotate",
          "axis": "x",
          "speed": "n_right / 60"
        },
        "mount": {
          "kind": "coaxial",
          "target": "carrier",
          "at": 0.72,
          "offset": 0
        },
        "shapes": [
          {
            "kind": "bevelGear",
            "rInner": 0.014,
            "h": 0.02,
            "teeth": "N_side",
            "module": 0.0038
          },
          {
            "kind": "cylinder",
            "position": [
              0,
              0.05,
              0
            ],
            "r": 0.015,
            "h": 0.12
          },
          {
            "kind": "tube",
            "position": [
              0,
              0.008,
              0
            ],
            "rOuter": 0.028,
            "rInner": 0.015,
            "h": 0.015
          }
        ]
      }
    ],
    "annotations": [
      {
        "id": "ann_torque_in",
        "kind": "moment",
        "label": "T_in",
        "magnitude": "input_torque",
        "unit": "N·m",
        "anchor": {
          "part": "ring_gear",
          "at": "center"
        }
      },
      {
        "id": "ann_t_left",
        "kind": "moment",
        "label": "T_L",
        "magnitude": "torque_per_wheel",
        "unit": "N·m",
        "anchor": {
          "part": "side_gear_left",
          "at": "start"
        }
      },
      {
        "id": "ann_t_right",
        "kind": "moment",
        "label": "T_R",
        "magnitude": "torque_per_wheel",
        "unit": "N·m",
        "anchor": {
          "part": "side_gear_right",
          "at": "end"
        }
      }
    ],
    "calculations": [
      {
        "id": "final_drive_ratio",
        "label": "Final drive ratio",
        "symbol": "i_fd",
        "formula": "N_ring / N_pinion",
        "unit": "",
        "latex": "i_{fd} = \\frac{z_r}{z_p}"
      },
      {
        "id": "n_left",
        "label": "Left axle speed",
        "symbol": "n_L",
        "formula": "input_rpm - delta_rpm / 2",
        "unit": "rpm",
        "latex": "n_L = n_c - \\frac{\\Delta n}{2}"
      },
      {
        "id": "n_right",
        "label": "Right axle speed",
        "symbol": "n_R",
        "formula": "input_rpm + delta_rpm / 2",
        "unit": "rpm",
        "latex": "n_R = n_c + \\frac{\\Delta n}{2}"
      },
      {
        "id": "torque_per_wheel",
        "label": "Axle torque per side",
        "symbol": "T_axle",
        "formula": "input_torque / 2",
        "unit": "N·m",
        "latex": "T_{axle} = \\frac{T_{in}}{2}"
      },
      {
        "id": "spider_spin",
        "label": "Spider relative spin",
        "symbol": "n_spider",
        "formula": "abs(delta_rpm) * (N_side / N_spider) / 2",
        "unit": "rpm",
        "latex": "n_s = \\frac{|\\Delta n|}{2} \\cdot \\frac{z_a}{z_s}"
      }
    ],
    "charts": [
      {
        "id": "axle_speeds",
        "title": "Left and Right Axle Speeds vs Speed Difference",
        "x": {
          "label": "Wheel speed differential Δn",
          "unit": "rpm",
          "from": "-150",
          "to": "150"
        },
        "y": {
          "label": "Axle speed",
          "unit": "rpm"
        },
        "series": [
          {
            "id": "s_left",
            "label": "Left axle speed (n_L)",
            "formula": "input_rpm - x / 2"
          },
          {
            "id": "s_right",
            "label": "Right axle speed (n_R)",
            "formula": "input_rpm + x / 2"
          }
        ]
      }
    ]
  },
  "view": {
    "camera": {
      "position": [
        0.38,
        0.28,
        0.44
      ],
      "target": [
        0,
        0,
        0
      ]
    },
    "extent": 0.48,
    "floorY": -0.22,
    "cut": {
      "enabled": true,
      "normal": [
        0,
        0,
        1
      ],
      "pos": 0.02
    }
  },
  "meta": {
    "generator": "Solidify (solidify.studio)",
    "license": "CC-BY-4.0",
    "created": "2026-11-10"
  }
}