Rotational Imbalance Detector
This rotational imbalance calculator helps identify the 1X imbalance signature at the running speed (f = RPM/60), check your rotor against an ISO 21940-11 balance grade (the permissible residual unbalance Uper = 1000·G·M/Ω in g·mm, with G in mm/s, M in kg, Ω in rad/s), and solve a single-plane trial-weight correction using the influence-coefficient method with genuine complex-vector math — magnitude and angle of the weight to add.
ℹ This is a calculator, not a measurement. It does not listen to your machine — you type in the vibration vectors (amplitude and phase) from your own calibrated instrument (an accelerometer/velocity probe plus a tachometer phase reference). The formulas are exact, but they assume an idealised single-plane, linear, rigid rotor. Real field balancing often needs two planes and a trim run, and you must verify your inputs — rotor mass, the correct ISO grade, and that both runs are at the same speed and phase reference. The 1X→imbalance and 2X→misalignment order mappings are common diagnostic conventions, not guarantees.
1X signature & ISO 21940-11 balance grade
Enter the running speed; add the rotor mass and pick a balance grade to get the permissible residual unbalance.
Single-plane trial-weight balance (influence-coefficient method)
From your instrument, enter the original 1X vibration vector O, then the vector T measured after adding a known trial weight at a known angle. Amplitude can be in any unit (mm/s, µm, mils…) as long as O and T use the same one; angles in degrees from your phase reference. Weight in any mass unit (g recommended).
ISO 21940-11:2012 balance-quality grades
Vibration order → likely source (diagnostic conventions)
How It Works
A rotor is unbalanced when its mass centre does not sit on its axis of rotation. As it spins, the offset mass throws a centrifugal force that rotates once per revolution — so imbalance appears in the vibration spectrum as a peak at the running speed, the 1X order: f1X = RPM/60 in hertz, with angular speed Ω = RPM·2π/60 in rad/s. (Use the RPM to Hz converter to look up the 1X through 10X harmonic frequencies for your machine before you start.) The hallmark of pure imbalance is a strong 1X with a steady phase that rotates with the shaft. Static imbalance means the heavy spot is in one axial plane (measured at one bearing); dynamic imbalance — the more common case in long rotors — means the heavy spot is spread across two axial planes, creating a couple that rocks the rotor even though it may be statically balanced. By contrast, misalignment usually adds a strong 2X (often with axial energy), and mechanical looseness raises a string of harmonics (3X, 4X…). Always confirm soft-foot (uneven base-plate contact) is corrected before a balance run; soft-foot can masquerade as imbalance by producing a 1X that shifts with each bolt-tightening sequence. Comparing the amplitude and phase of these orders is how you decide whether the problem is really imbalance before you start adding weights.
How much residual imbalance is acceptable is set by a balance-quality grade in ISO 21940-11:2012 (which replaced ISO 1940-1). Each grade G is a velocity number in mm/s equal to the product of the permissible specific unbalance (in mm) and the angular speed, G = eper[mm]·Ω. Rearranged and converted to the usual micrometre units, the permissible specific unbalance is eper = 1000·G/Ω (in µm, numerically the same as g·mm/kg of mass-centre eccentricity), and the permissible residual unbalance for a rotor of mass M is Uper = eper·M = 1000·G·M/Ω (in g·mm, with G in mm/s, M in kg, Ω in rad/s — the ×1000 converts the raw mm·kg product to g·mm). A faster rotor, or a tighter grade, leaves you a smaller allowance. The grade you pick must match the machine type — the table above lists the real published examples, from G 0.4 for precision grinder spindles up to G 4000 for slow marine diesels.
To actually correct imbalance, this tool uses the single-plane influence-coefficient method, which treats the rotor as a linear system using complex (vector) arithmetic. You record the original 1X vibration as a vector O (amplitude ∠ phase). You then bolt a known trial weight Wt at a known angle α and re-measure, getting a new vector T. The change the weight caused is ΔV = T − O, so the rotor’s influence coefficient — the vibration produced per unit of weight, including the lag angle — is H = (T − O)/(Wt∠α). The weight that would cancel the original vibration is then Wc = −O/H, reported as a magnitude and an angle. If the trial run barely changed the reading (ΔV ≈ 0) the coefficient is undefined and the tool refuses to divide by zero — that is your cue to use a bigger trial weight or a different angle.
Two honest cautions. First, all of this is the idealised, linear, single-plane model: it assumes a rigid rotor whose response scales perfectly with the added weight, measured at one bearing in one direction. Long or flexible rotors generally need two-plane (or modal) balancing, and even an ideal single-plane job usually needs a trim run to chase out residual error. Operating near a critical speed (a rotordynamic resonance) will invalidate the linearity assumption because the influence coefficient changes with speed around the resonance, so the correction calculated away from the critical will not transfer cleanly. Second, this page computes nothing from your machine — the quality of the answer is entirely the quality of the vibration vectors you measure with a proper instrument and a stable tachometer phase reference. After you fit the correction weight you should always verify with a final run and check the residual vibration against the ISO 21940-11 limit for your grade. For assessing whether the resulting vibration level is acceptable by machine class, the Vibration Severity Checker applies the ISO 10816 mm/s zones to your post-balance reading. Use it to plan and check a rotor balancing job, not as a substitute for a calibrated balancer.