{
  "$schema": "https://slfy.solidify.studio/schema/slfy-0.1.schema.json",
  "format": "slfy",
  "version": "0.1",
  "model": {
    "id": "muff-coupling",
    "title": "Rigid Sleeve (Muff) Coupling",
    "summary": "A rigid sleeve coupling connecting two collinear 30 mm shafts via a solid cast iron sleeve and a sunk key, featuring torsional shear and crushing stress analyses.",
    "units": "mm",
    "parameters": [
      {
        "id": "d",
        "label": "Shaft diameter",
        "symbol": "d",
        "value": 30,
        "min": 20,
        "max": 50,
        "step": 2,
        "unit": "mm"
      },
      {
        "id": "T",
        "label": "Transmitted torque",
        "symbol": "T",
        "value": 150,
        "min": 20,
        "max": 400,
        "step": 10,
        "unit": "N·m"
      },
      {
        "id": "L_sleeve",
        "label": "Sleeve length",
        "symbol": "L",
        "value": 105,
        "min": 70,
        "max": 160,
        "step": 5,
        "unit": "mm"
      },
      {
        "id": "D_outer",
        "label": "Sleeve outer diameter",
        "symbol": "D",
        "value": 72,
        "min": 50,
        "max": 110,
        "step": 2,
        "unit": "mm"
      },
      {
        "id": "w_key",
        "label": "Key width",
        "symbol": "w",
        "value": 8,
        "min": 6,
        "max": 14,
        "step": 1,
        "unit": "mm"
      },
      {
        "id": "h_key",
        "label": "Key height",
        "symbol": "h",
        "value": 7,
        "min": 5,
        "max": 12,
        "step": 1,
        "unit": "mm"
      }
    ],
    "parts": [
      {
        "id": "sleeve",
        "name": "Cast iron sleeve",
        "material": "castIron",
        "role": "housing",
        "position": [
          0,
          0,
          0
        ],
        "rotation": [
          0,
          0,
          1.5708
        ],
        "explode": [
          0,
          0.08,
          0
        ],
        "cut": true,
        "info": {
          "summary": "Cast iron hollow sleeve (muff)",
          "role": "Encloses the shaft ends and transmits torque across the junction through the key."
        },
        "shapes": [
          {
            "kind": "tube",
            "rOuter": "D_outer / 2000",
            "rInner": "d / 2000",
            "h": "L_sleeve / 1000"
          },
          {
            "kind": "box",
            "op": "subtract",
            "position": [
              "d / 2000 + h_key / 4000",
              0,
              0
            ],
            "sx": "h_key / 2000 + 0.002",
            "sy": "L_sleeve / 1000 + 0.002",
            "sz": "w_key / 1000"
          },
          {
            "kind": "cylinder",
            "op": "subtract",
            "position": [
              "D_outer / 4000",
              0,
              0
            ],
            "r": 0.004,
            "h": "D_outer / 1000"
          }
        ]
      },
      {
        "id": "shaft_in",
        "name": "Driving shaft",
        "material": "steel",
        "role": "moving",
        "explode": [
          -0.1,
          0,
          0
        ],
        "cut": false,
        "info": {
          "summary": "Driving input shaft",
          "role": "Transfers rotational power from the driver into the coupling assembly."
        },
        "motion": {
          "kind": "rotate",
          "axis": "x",
          "speed": 1
        },
        "mount": {
          "kind": "coaxial",
          "target": "sleeve",
          "at": 0.5,
          "offset": -0.082
        },
        "shapes": [
          {
            "kind": "cylinder",
            "r": "d / 2000",
            "h": 0.16
          },
          {
            "kind": "box",
            "op": "subtract",
            "position": [
              "d / 2000 - h_key / 4000",
              "0.08 - L_sleeve / 4000",
              0
            ],
            "sx": "h_key / 2000 + 0.001",
            "sy": "L_sleeve / 2000 + 0.002",
            "sz": "w_key / 1000"
          }
        ]
      },
      {
        "id": "shaft_out",
        "name": "Driven shaft",
        "material": "steel",
        "role": "moving",
        "explode": [
          0.1,
          0,
          0
        ],
        "cut": false,
        "info": {
          "summary": "Driven output shaft",
          "role": "Receives torque through the coupling to drive the attached load."
        },
        "motion": {
          "kind": "rotate",
          "axis": "x",
          "speed": 1
        },
        "mount": {
          "kind": "coaxial",
          "target": "sleeve",
          "at": 0.5,
          "offset": 0.082
        },
        "shapes": [
          {
            "kind": "cylinder",
            "r": "d / 2000",
            "h": 0.16
          },
          {
            "kind": "box",
            "op": "subtract",
            "position": [
              "d / 2000 - h_key / 4000",
              "-0.08 + L_sleeve / 4000",
              0
            ],
            "sx": "h_key / 2000 + 0.001",
            "sy": "L_sleeve / 2000 + 0.002",
            "sz": "w_key / 1000"
          }
        ]
      },
      {
        "id": "key",
        "name": "Sunk key",
        "material": "steelDark",
        "role": "moving",
        "explode": [
          0,
          0.07,
          0
        ],
        "cut": false,
        "info": {
          "summary": "Parallel sunk key",
          "role": "Bridges both shafts and the sleeve bore to transmit torque by shear and bearing."
        },
        "motion": {
          "kind": "rotate",
          "axis": "x",
          "speed": 1
        },
        "mount": {
          "kind": "coaxial",
          "target": "sleeve",
          "at": 0.5,
          "shift": [
            "d / 2000",
            0,
            0
          ]
        },
        "shapes": [
          {
            "kind": "box",
            "sx": "h_key / 1000",
            "sy": "L_sleeve / 1000 - 0.004",
            "sz": "w_key / 1000"
          }
        ]
      },
      {
        "id": "setscrew",
        "name": "Locking setscrew",
        "material": "steelMatte",
        "role": "static",
        "explode": [
          0,
          0.11,
          0
        ],
        "cut": false,
        "info": {
          "summary": "Socket head setscrew",
          "role": "Clamps radially against the key to prevent axial wandering of the sleeve."
        },
        "mount": {
          "kind": "coaxial",
          "target": "sleeve",
          "at": 0.5,
          "shift": [
            "D_outer / 2000 - 0.004",
            0,
            0
          ]
        },
        "shapes": [
          {
            "kind": "cylinder",
            "r": 0.0038,
            "h": 0.014
          }
        ]
      }
    ],
    "annotations": [
      {
        "id": "t_in",
        "kind": "moment",
        "label": "T",
        "magnitude": "T",
        "unit": "N·m",
        "anchor": {
          "part": "shaft_in",
          "at": "start"
        }
      },
      {
        "id": "t_out",
        "kind": "moment",
        "label": "T_{out}",
        "magnitude": "T",
        "unit": "N·m",
        "anchor": {
          "part": "shaft_out",
          "at": "end"
        }
      },
      {
        "id": "sleeve_len",
        "kind": "dimension",
        "label": "L",
        "magnitude": "L_sleeve",
        "unit": "mm",
        "anchor": {
          "part": "sleeve",
          "at": "center"
        }
      }
    ],
    "calculations": [
      {
        "id": "tau_shaft",
        "label": "Shaft shear stress",
        "symbol": "\\tau_s",
        "formula": "16 * T / (pi * (d / 1000)^3) / 1000000",
        "unit": "MPa",
        "latex": "\\tau_s = \\frac{16 T}{\\pi d^3}",
        "limit": {
          "kind": "max",
          "value": 60,
          "label": "Allowable shaft shear stress"
        }
      },
      {
        "id": "tau_sleeve",
        "label": "Sleeve shear stress",
        "symbol": "\\tau_m",
        "formula": "16 * T * (D_outer / 1000) / (pi * ((D_outer / 1000)^4 - (d / 1000)^4)) / 1000000",
        "unit": "MPa",
        "latex": "\\tau_m = \\frac{16 T D}{\\pi (D^4 - d^4)}",
        "limit": {
          "kind": "max",
          "value": 15,
          "label": "Allowable cast iron shear stress"
        }
      },
      {
        "id": "tau_key",
        "label": "Key shear stress",
        "symbol": "\\tau_k",
        "formula": "2 * T / ((d / 1000) * (w_key / 1000) * (L_sleeve / 1000)) / 1000000",
        "unit": "MPa",
        "latex": "\\tau_k = \\frac{2 T}{d \\cdot w \\cdot L}",
        "limit": {
          "kind": "max",
          "value": 45,
          "label": "Allowable key shear stress"
        }
      },
      {
        "id": "sigma_crush",
        "label": "Key crushing stress",
        "symbol": "\\sigma_c",
        "formula": "4 * T / ((d / 1000) * (h_key / 1000) * (L_sleeve / 1000)) / 1000000",
        "unit": "MPa",
        "latex": "\\sigma_c = \\frac{4 T}{d \\cdot h \\cdot L}",
        "limit": {
          "kind": "max",
          "value": 90,
          "label": "Allowable key compressive stress"
        }
      }
    ],
    "charts": [
      {
        "id": "stress_curve",
        "title": "Component Stresses vs Transmitted Torque",
        "x": {
          "label": "Torque",
          "unit": "N·m",
          "from": 20,
          "to": 350
        },
        "y": {
          "label": "Stress",
          "unit": "MPa"
        },
        "series": [
          {
            "id": "s_shaft",
            "label": "Shaft shear stress",
            "formula": "16 * x / (pi * (d / 1000)^3) / 1000000"
          },
          {
            "id": "s_key",
            "label": "Key shear stress",
            "formula": "2 * x / ((d / 1000) * (w_key / 1000) * (L_sleeve / 1000)) / 1000000"
          },
          {
            "id": "s_crush",
            "label": "Key crushing stress",
            "formula": "4 * x / ((d / 1000) * (h_key / 1000) * (L_sleeve / 1000)) / 1000000"
          },
          {
            "id": "s_sleeve",
            "label": "Sleeve shear stress",
            "formula": "16 * x * (D_outer / 1000) / (pi * ((D_outer / 1000)^4 - (d / 1000)^4)) / 1000000"
          }
        ]
      }
    ]
  },
  "view": {
    "camera": {
      "position": [
        0.32,
        0.22,
        0.38
      ],
      "target": [
        0,
        0,
        0
      ]
    },
    "extent": 0.45,
    "floorY": -0.15,
    "cut": {
      "enabled": true,
      "normal": [
        0,
        0,
        1
      ],
      "pos": 0.001
    }
  },
  "meta": {
    "generator": "Solidify (solidify.studio)",
    "license": "CC-BY-4.0",
    "created": "2026-11-10"
  }
}