{
  "doc": {
    "type": "doc",
    "content": [
      {
        "type": "paragraph",
        "attrs": {
          "textAlign": "left"
        },
        "content": [
          {
            "type": "text",
            "text": "A 10hp three-phase induction motor has a rotor diameter of D "
          },
          {
            "type": "inlineMath",
            "attrs": {
              "mathType": "asciimath"
            },
            "content": [
              {
                "type": "text",
                "text": "= 5.7"
              }
            ]
          },
          {
            "type": "text",
            "text": " in, an active core length of L "
          },
          {
            "type": "inlineMath",
            "attrs": {
              "mathType": "asciimath"
            },
            "content": [
              {
                "type": "text",
                "text": "= 6"
              }
            ]
          },
          {
            "type": "text",
            "text": " in, a radial air gap length of"
          },
          {
            "type": "hardBreak"
          },
          {
            "type": "text",
            "text": "g "
          },
          {
            "type": "inlineMath",
            "attrs": {
              "mathType": "asciimath"
            },
            "content": [
              {
                "type": "text",
                "text": "= 0.0185"
              }
            ]
          },
          {
            "type": "text",
            "text": " in, and a stator core containing S "
          },
          {
            "type": "inlineMath",
            "attrs": {
              "mathType": "asciimath"
            },
            "content": [
              {
                "type": "text",
                "text": "= 48"
              }
            ]
          },
          {
            "type": "text",
            "text": " slots. The machine is designed as a four-pole (P "
          },
          {
            "type": "inlineMath",
            "attrs": {
              "mathType": "asciimath"
            },
            "content": [
              {
                "type": "text",
                "text": "="
              }
            ]
          },
          {
            "type": "text",
            "text": " 4), consequent-pole motor. Each"
          },
          {
            "type": "hardBreak"
          },
          {
            "type": "text",
            "text": "phase winding consists of two coil groups, with each group comprising six concentric coils having turn counts"
          },
          {
            "type": "hardBreak"
          },
          {
            "type": "text",
            "text": "{N\u2081, "
          },
          {
            "type": "inlineMath",
            "attrs": {
              "mathType": "asciimath"
            },
            "content": [
              {
                "type": "text",
                "text": "N\u2082, N\u2083, N\u2084, N\u2085, N\u2086} = {6"
              }
            ]
          },
          {
            "type": "text",
            "text": ", 12, 18, 18, 12, 6}turns"
          },
          {
            "type": "hardBreak"
          },
          {
            "type": "text",
            "text": "and corresponding coil spans of: {W\u2081, "
          },
          {
            "type": "inlineMath",
            "attrs": {
              "mathType": "asciimath"
            },
            "content": [
              {
                "type": "text",
                "text": "W\u2082, W\u2083, W\u2084, W\u2085, W\u2086} = {17"
              }
            ]
          },
          {
            "type": "text",
            "text": ", 15, 13, 11, 9, 7}slots"
          },
          {
            "type": "hardBreak"
          },
          {
            "type": "text",
            "text": "respectively."
          },
          {
            "type": "hardBreak"
          },
          {
            "type": "text",
            "text": "(a) Determine the complete stator winding arrangement (including the pole pitch, slot electrical angle, and coil pitch angles), and calculate the"
          },
          {
            "type": "hardBreak"
          },
          {
            "type": "text",
            "text": "overall fundamental winding factor "
          },
          {
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            "attrs": {
              "mathType": "asciimath"
            },
            "content": [
              {
                "type": "text",
                "text": "k_w"
              }
            ]
          },
          {
            "type": "text",
            "text": " for this stepped, concentric winding, accounting for the unequal turns, individual coil pitches, and phase"
          },
          {
            "type": "hardBreak"
          },
          {
            "type": "text",
            "text": "belt distribution."
          },
          {
            "type": "hardBreak"
          },
          {
            "type": "text",
            "text": "(b) Derive the expression for the fundamental air-gap magnetomotive force (MMF) produced by this winding arrangement, and establish"
          },
          {
            "type": "hardBreak"
          },
          {
            "type": "text",
            "text": "quantitatively how this non-uniform concentric coil distribution affects the fundamental air-gap MMF amplitude and space harmonic content"
          },
          {
            "type": "hardBreak"
          },
          {
            "type": "text",
            "text": "compared to an equivalent uniformly distributed, full-pitch winding."
          }
        ]
      }
    ]
  },
  "timestamp": 1792161000000,
  "type": "QUESTION",
  "title": "10hp Three-Phase Induction Motor"
}