Permissible Residual Unbalance and Balance Grade

The residual unbalance a rotor is allowed at its operating speed, and what that works out to in grams on the balancing machine. A balance grade is defined as the permissible eccentricity multiplied by the angular velocity, expressed in millimetres per second, so a grade of 6.3 means the center of mass may sit off the axis by however much gives 6.3 mm/s of rim velocity at operating speed. The grades are a published ladder: G6.3 for general machinery, pumps, and fans; G2.5 for machine tool drives, turbines, and better electric motors; G1 and G0.4 for grinding spindles and precision equipment. The important consequence is in the division. Permissible eccentricity is inversely proportional to speed, so DOUBLING the rotor speed HALVES the allowable unbalance -- a fan balanced to G6.3 at 1,800 rpm and then run at 3,600 rpm is not at G6.3 any more, it is at G12.6, one full grade coarser, and it will vibrate accordingly. That is why rebalancing is required after a speed change and why a two-speed machine is balanced to its high speed. The last lines translate the tolerance into something an operator can act on: a 50 kg rotor at 3,600 rpm to G6.3, corrected in two planes at a 150 mm radius, allows 836 g-mm total, 418 per plane, which is 2.79 g at that radius -- about the mass of a small washer, and a good sense of how little material puts a rotor out of tolerance. A tolerance calculation; ISO 1940 in full, the machine's own vibration criteria, and the balancing machine's readout govern.

omega_rad_s = 2 pi rpm / 60; e_permissible = balance_grade x 1000 / omega (g-mm per kg); u_permissible = e_permissible x rotor_mass_kg; per plane = u_permissible / planes; correction_mass_g = per plane / correction_radius_mm.

ISO 1940-1 permissible residual unbalance -- the balance grade G is the permissible eccentricity times the angular velocity in mm/s, so e = G x 1000 / omega in g-mm per kg -- cited by name and not reproduced. The grade ladder is named and the grade is entered rather than looked up. ISO 1940 in full, the machine's vibration criteria, and the balancing machine's readout govern.

The relation is arithmetic once the grade is chosen; the standard's grade table is cited rather than mirrored, and the rotor's own mass, speed, and correction geometry are the user's values.

Estimate. AHJ and licensed professional govern.

Field names used by the API: balance_grade, rpm, rotor_mass_kg, planes, correction_radius_mm, omega_rad_s, e_permissible, u_permissible, per_plane, correction_mass_g

• Grade definition G is permissible eccentricity times angular velocity in mm/s; e = G x 1000 / omega in g-mm per kgISO 1940-1
• Inverse in speed doubling the speed halves the allowable unbalance; a speed change forces a rebalanceISO 1940-1
• Rigid rotor the two-plane correction assumes a rigid rotor below its first critical speed; a flexible rotor is a different problembalancing practice