High-Speed Bearing Inertial and Gyroscopic Effects Calculator

Content

Geometry and operating inputs

Results update automatically. Enter internal bearing geometry rather than a designation.

Screening result

Per-element force balance at the entered steady speeds.

Result—

Method, assumptions and use

The calculator resolves centrifugal force against the supplied contact geometry and applied per-element load. Gyroscopic resistance compares a solid-ball inertial moment with the resisting moment available at two race contacts.

Stle
Fc,ball = 2.26 × 10−11D³dmnm²
Fc,roller = 3.39 × 10−11D²ltdmnm²
cot αo = cot αi + Fc/Qia
μreq = 2Mg / [D(Qi + Qo)]
  • Dimensions are in millimetres, speeds in rpm and loads in newtons; the historical coefficients represent nominal steel rolling elements.
  • Steady speed, rigid supplied geometry and quasi-static force balance are assumed.
  • Contact deformation, skidding, lubrication traction, thermal growth, cage flexibility and fatigue life are excluded.

Use these values to identify when rolling-element inertia may require a complete coupled bearing equilibrium, contact, traction and thermal analysis. Do not interpret a friction threshold as the actual lubricant traction coefficient.

Reference

Harris, T. A. and Kotzalas, M. N. (2006), Advanced Concepts of Bearing Technology: Rolling Bearing Analysis, Fifth Edition, CRC Press, Chapter 3, especially Equations 3.27, 3.32–3.34, 3.38, 3.43–3.44 and 3.67. doi:10.1201/9781420006582.

Related tools: bearing kappa factor and the TriboNet calculator directory.

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