{
  "review_date": "2026-10-04",
  "results_scope": "Development-solver reference results: equation teaching cases, historical chart comparisons and an independently audited published centered-thrust scalar; model differences and unresolved offsets are retained.",
  "source_urls": [
    "https://ntrs.nasa.gov/citations/19640005312",
    "https://archive.org/details/DTIC_AD0466393",
    "https://doi.org/10.1155/2009/471804",
    "https://ntrs.nasa.gov/citations/20150018925",
    "https://doi.org/10.2495/TD100191",
    "https://doi.org/10.1155/2016/2106810",
    "https://journals.sagepub.com/doi/10.1177/16878132221132951",
    "https://journals.sagepub.com/doi/10.1177/16878132241275608",
    "https://ntrs.nasa.gov/citations/20120008398",
    "https://past.isma-isaac.be/downloads/isma2022/proceedings/Contribution_183_proceeding_3.pdf",
    "https://journals.sagepub.com/doi/full/10.1177/1687814018798973",
    "https://www.mdpi.com/1996-1944/13/18/4075",
    "https://doi.org/10.1016/j.jksues.2018.03.002"
  ],
  "stiffness_definition": "Central derivative of actual bearing reaction versus solved displacement. Source values use requested nominal loads; legacy resultant offsets are reported.",
  "material_boundary": {
    "active_contact_temperature_F": 100,
    "active_steel_density_lb_per_in3": 0.283,
    "active_steel_E_psi": 30402585.65,
    "active_steel_Poisson_ratio": 0.29597333470826115,
    "historical_Jones_reference_E_psi": 29000000,
    "historical_Jones_reference_Poisson_ratio": 0.25,
    "AFAPL_deflection_coefficient": 7.8107e-06,
    "note": "MAINBALL replaces E for the steel density and all Poisson ratios at 100 F. The historical source coefficient has not been reproduced by a selectable constitutive model."
  },
  "static_boundary": "60 rpm reporting surrogate; each document checked again at 6 rpm. Exactly zero rpm fails in the inherited reporting path.",
  "chart_review_relative_limit": 0.1,
  "inputs": [
    {
      "filename": "radial-load-distribution.bearing",
      "sha256": "0f3c3d970ca8204cce6fafcec2fba23912a2c50a6fa89cf550a9df6a046c0339"
    },
    {
      "filename": "uniform-thrust.bearing",
      "sha256": "d490b2c3f3a0301a47e9f3a058a81a75716d676f95ce8519704dcd35ec0a0065"
    },
    {
      "filename": "rotating-outer-ring.bearing",
      "sha256": "61d42a484a61f1791fac1a7c8c1e64d2eec2c3acbcae7697b9800ce4a0488b44"
    },
    {
      "filename": "a2-radial-100.bearing",
      "sha256": "deb8d41e1c7890df530cf0dd97b685ae751a495d4cd5bfca6916f96291fd043e"
    },
    {
      "filename": "a2-radial-700.bearing",
      "sha256": "f64aa34d1daee640eefd5da1ab7e5b2f55e884244e03511188b1e0d8c72c4328"
    },
    {
      "filename": "a2-thrust-100.bearing",
      "sha256": "2c94af612c118055ed8abcda266c456491c01238e7b7c834300e3ff1799c35bb"
    },
    {
      "filename": "a2-thrust-700.bearing",
      "sha256": "f5d0e83ddfcc35053336b586e56e54e4ace03d48f949f3216320a8d5227ec040"
    },
    {
      "filename": "a2-thrust-pair-member-200.bearing",
      "sha256": "45d94f09c5a525a3c1b0064c0e4d46123380436cb00e322332b76ff8a3dfce51"
    },
    {
      "filename": "pa2-fixed-axial-radial-100.bearing",
      "sha256": "dd3fa072acb930699906264bc6c81d8e11eae4e257afa4f399d88885cac077df"
    },
    {
      "filename": "pa2-fixed-axial-radial-700.bearing",
      "sha256": "82ee8c5bbcd6631b79ef18039da0ebc2b7bdec716e0cd20bf164b9ef55470032"
    },
    {
      "filename": "ricci-centered-thrust-17800.bearing",
      "sha256": "80dfb801ed8542d6060b791b38fb56df6df36aeecd0700f2f6bd496e70e53152"
    },
    {
      "filename": "hou2024-positive-1000.bearing",
      "sha256": "4639bd865ab0c7288e4bdba2b6b4f13a53562942043b556df932e79613b2427e"
    },
    {
      "filename": "hou2024-positive-5000.bearing",
      "sha256": "d6d243b3a1a22c2b055ae27dc8ea4c37ff3f48c41336717c91f2a24f1a969590"
    },
    {
      "filename": "hou2024-positive-10000.bearing",
      "sha256": "d800e1959958913d7517c6243af5bc50e3e5502b99b3fa9f370116a06534c145"
    },
    {
      "filename": "hou2024-negative-1000.bearing",
      "sha256": "49c5892ad69b2282116e28d515ae0f53d997f863bc206cbe57255162fbaa8905"
    },
    {
      "filename": "hou2024-negative-5000.bearing",
      "sha256": "1fb4a45a3a82062365cb056fac31184704ee54dc7121686536fb5916d561cc84"
    },
    {
      "filename": "hou2024-negative-10000.bearing",
      "sha256": "a622a79ce60c8cfe05b807ab970b279f2a8cd083320ece3b710a0a282fdba360"
    },
    {
      "filename": "nasa2012-ball-clearance-627.bearing",
      "sha256": "be8c91c4af48e85d83af80cbdee54813c7516b2f227e469a486266dd0ebf1749"
    }
  ],
  "NASA_equation_checks": [
    {
      "id": "radial-load-distribution",
      "reference": "Chapter 6, printed pp.165-166, eqs.6-52 through 6-60; PDF pp.169-170",
      "requested_resultant_lbf": 100.0,
      "computed_inner_resultant_lbf": 100.62791970528286,
      "relative_resultant_offset": 0.0062791970528286445,
      "expected_nominal_cage_rpm": 23.767806267806264,
      "computed_nominal_cage_rpm": 23.767797189176907,
      "detail": {
        "ideal_maximum_inner_load_lbf": 48.7245335957625,
        "computed_maximum_inner_load_lbf": 49.030529315777585,
        "finite_ball_count_factor": 4.385208023618626,
        "maximum_normalized_distribution_error": 2.247900785137813e-06,
        "distribution_error_limit": 5e-06
      }
    },
    {
      "id": "uniform-thrust",
      "reference": "Chapter 6, printed p.166, eq.6-61; PDF p.170",
      "requested_resultant_lbf": 100.0,
      "computed_inner_resultant_lbf": 100.59001103404493,
      "relative_resultant_offset": 0.005900110340449238,
      "expected_nominal_cage_rpm": 24.602761906614074,
      "computed_nominal_cage_rpm": 24.60275249518957,
      "detail": {
        "computed_inner_load_per_ball_lbf": 21.844554780865764,
        "operating_inner_contact_angle_degrees": 30.7734971615703,
        "inner_load_spread_lbf": 0.0
      }
    },
    {
      "id": "rotating-outer-ring",
      "reference": "Chapter 6, printed pp.159-160, eq.6-44; PDF pp.163-164",
      "requested_resultant_lbf": 100.0,
      "computed_inner_resultant_lbf": 100.5916684209724,
      "relative_resultant_offset": 0.005916684209724021,
      "expected_nominal_cage_rpm": 353.97238093385926,
      "computed_nominal_cage_rpm": 353.97224586508435,
      "detail": {
        "computed_inner_load_per_ball_lbf": 21.82118813584818,
        "operating_inner_contact_angle_degrees": 30.810602769712556,
        "inner_load_spread_lbf": 0.0
      }
    }
  ],
  "AFAPL_stiffness_comparisons": [
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      "source_case_id": "G001",
      "title": "AFAPL Part IV: a2 radial 100",
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      "computed_stiffness_lbf_per_in": 304416.66831952403,
      "relative_published_difference": 0.057002320553902974,
      "review_status": "Approximate chart agreement; teaching use",
      "base_point": {
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        "requested_axial_load_lbf": 0.0,
        "actual_axial_reaction_lbf": 0,
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        "axial_displacement_in": 0,
        "radial_displacement_in": 0.0004957570355670079,
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      "id": "A004",
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    {
      "id": "A005",
      "source_case_id": "G003",
      "title": "AFAPL Part IV: a2 thrust pair member 200",
      "kind": "pair-member",
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      "computed_stiffness_lbf_per_in": 148148.88590092896,
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      "review_status": "Approximate chart agreement; teaching use",
      "base_point": {
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        "requested_axial_load_lbf": 200.0,
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