Ideal synchronous excitation arithmetic
Rotating-Unbalance Force Amplitude
Evaluate F̂ = Uω² from a specified unbalance magnitude and constant speed. The result is an ideal rotating excitation magnitude—not a bearing reaction, vibration response or acceptance verdict.
Ideal force amplitude
Amplitude only. Direction rotates at 1× speed for this ideal single-vector representation.
Mass-eccentricity arithmetic
For uniform circular motion, the NASA circular-motion derivation gives the required force magnitude as mω²r. Substituting the mass-eccentricity product U = m·e gives F̂ = Uω². In an inertial frame the supporting reaction is centripetal; “centrifugal force” is the corresponding rotating-frame description.
Jednostki
g·mm is converted by 10⁻⁶ kg·m. For avoirdupois oz·in, this page uses 1 oz = 0.028349523125 kg and 1 in = 0.0254 m, hence 1 oz·in = 720.077887375 g·mm. The exact base conversions are documented by NIST SP 811 conversion factors.
ISO and system boundary
ISO 21940-2:2017, confirmed in 2022, is the current balancing vocabulary standard. ISO 21940-11:2016 with Amendment 1:2022 covers rigid-behaviour rotor balancing procedures, tolerances, correction planes, allocation and errors. This arithmetic neither reproduces those procedures nor establishes compliance.
Not a bearing or vibration model: bearing reactions and transmitted forces depend on the axial/vector distribution of unbalance, rotor geometry, support stiffness and damping, modes, speed and other loads. Vibration displacement, velocity, acceleration, stress and bearing life require a validated dynamic model or measurements. Flexible behaviour and unbalance couples cannot be reduced to one scalar output here.
Checked example
For U = 1000 g·mm and n = 3000 rpm: U = 0.001 kg·m, ω = 314.159265 rad/s, and F̂ = 98.696044 N.
