{
  "schema_version": 1,
  "review_date": "2026-10-04",
  "document_kind": "Published source data for research examples",
  "title": "A discrete calculation method for radial load distribution integral of radial bearings",
  "authors": "Yu Hou; Yi Yin; Xi Wang",
  "year": "2024",
  "source_url": "https://journals.sagepub.com/doi/10.1177/16878132241275608",
  "review_scope": "Publisher full-text assumptions and Tables 1–5; independent force projection of the rounded corrected-integral ball loads; PDF endpoint returned HTTP 403",
  "readiness": "Runnable static ball-contact comparison; source model differences retained",
  "remaining_inputs": [
    "Exact constitutive/elliptic matching for each contact",
    "Preserve negative-table force residuals",
    "Complete NU209 roller geometry"
  ],
  "paper_id": "P014",
  "filename": "hou2024-source-cases.json",
  "website_anchor": "hou-clearance",
  "source_location": "Table 1 geometry; corrected-integral columns of Tables 2 and 3",
  "native_input_available": true,
  "geometry": {
    "designation": "6209",
    "ball_count": 9,
    "ball_diameter_mm": 12.7,
    "inner_race_diameter_mm": 52.292,
    "outer_race_diameter_mm": 77.706,
    "inner_groove_radius_mm": 6.6,
    "outer_groove_radius_mm": 6.6,
    "azimuth_increment_degrees": 40,
    "load_aligned_ball_azimuth_degrees": 0
  },
  "ball_load_table_audit_filename": "hou2024-table-force-check.json",
  "ball_load_table_definition": "Each nonzero-azimuth value represents the symmetric pair at plus and minus that azimuth. Blank source entries are unloaded positions. The source-table audit preserves force residuals.",
  "roller_geometry_partial": {
    "designation": "NU209",
    "roller_count": 14,
    "effective_length_mm": 9.601,
    "positive_diametral_clearance_mm": 0.04,
    "negative_diametral_clearance_mm": -0.01,
    "radial_loads_n": [
      1000,
      5000,
      10000
    ],
    "remaining_geometry": "Roller diameter, raceway/pitch geometry and material/contact conventions require recovery. No dimensions are borrowed from another NU209 paper."
  },
  "comparison_boundary": "Maven 52100 steel law at 100 F: E approximately 209618 MPa and nu 0.2959733. NASA source E 205900 MPa and nu 0.3. Maven elliptic iteration and deformed pitch differ from Hou fixed stiffness/Brewe-Hamrock approximation. All loaded-ball counts agree; small edge-of-zone loads require individual review. NASA continuous approximation is distinct from discrete equilibrium; rollers and life remain unqualified.",
  "ball_load_cases": [
    {
      "radial_load_n": 1000,
      "diametral_clearance_mm": 0.015,
      "published_unique_loads_n_at_0_40_80_120_degrees": [
        565.102,
        283.859
      ],
      "loaded_ball_count": 3,
      "projected_radial_reaction_n": 999.9992191586199,
      "relative_force_residual": -7.808413801058123e-07,
      "within_1e_minus_6_relative_force_screen": true
    },
    {
      "radial_load_n": 5000,
      "diametral_clearance_mm": 0.015,
      "published_unique_loads_n_at_0_40_80_120_degrees": [
        2589.31,
        1573.419,
        0.215
      ],
      "loaded_ball_count": 5,
      "projected_radial_reaction_n": 5000.002432012036,
      "relative_force_residual": 4.864024071139283e-07,
      "within_1e_minus_6_relative_force_screen": true
    },
    {
      "radial_load_n": 10000,
      "diametral_clearance_mm": 0.015,
      "published_unique_loads_n_at_0_40_80_120_degrees": [
        5073.518,
        3196.93,
        82.078
      ],
      "loaded_ball_count": 5,
      "projected_radial_reaction_n": 10000.0043133338,
      "relative_force_residual": 4.313333800382679e-07,
      "within_1e_minus_6_relative_force_screen": true
    },
    {
      "radial_load_n": 1000,
      "diametral_clearance_mm": -0.01,
      "published_unique_loads_n_at_0_40_80_120_degrees": [
        432.585,
        352.798,
        176.981,
        34.469
      ],
      "loaded_ball_count": 7,
      "projected_radial_reaction_n": 1000.0987511503204,
      "relative_force_residual": 9.875115032036774e-05,
      "within_1e_minus_6_relative_force_screen": false
    },
    {
      "radial_load_n": 5000,
      "diametral_clearance_mm": -0.01,
      "published_unique_loads_n_at_0_40_80_120_degrees": [
        2320.97,
        1663.6,
        375.306
      ],
      "loaded_ball_count": 5,
      "projected_radial_reaction_n": 5000.095477080393,
      "relative_force_residual": 1.9095416078562266e-05,
      "within_1e_minus_6_relative_force_screen": false
    },
    {
      "radial_load_n": 10000,
      "diametral_clearance_mm": -0.01,
      "published_unique_loads_n_at_0_40_80_120_degrees": [
        4728.94,
        3306.271,
        592.111
      ],
      "loaded_ball_count": 5,
      "projected_radial_reaction_n": 10000.07904624394,
      "relative_force_residual": 7.904624393995618e-06,
      "within_1e_minus_6_relative_force_screen": false
    }
  ],
  "native_input_filenames": [
    "hou2024-positive-1000.bearing",
    "hou2024-positive-5000.bearing",
    "hou2024-positive-10000.bearing",
    "hou2024-negative-1000.bearing",
    "hou2024-negative-5000.bearing",
    "hou2024-negative-10000.bearing"
  ],
  "native_comparison_filename": "radial-clearance-comparison.json",
  "source_combined_stiffness_n_per_mm_power_1_5": 377725.62437407504,
  "derived_pitch_diameter_mm": 64.999
}