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Static versus dynamic balancing

Short answer

Static balancing eliminates the resultant centrifugal force (Σmr=0) for coplanar masses; dynamic balancing also eliminates the resultant couple (Σmrl=0), requiring two correction planes. Dynamic balance ensures static balance, not conversely. Complete balance: vector sum of centrifugal forces = 0 and vector sum of couples about any plane = 0.

Differentiate between static balancing and dynamic balancing of rotating masses. State the conditions for complete balance of several masses rotating in different planes.

Unbalanced rotating masses produce a centrifugal force mrω2mr\omega^2 that rotates with the shaft and loads the bearings. Balancing removes it.

Static vs dynamic balancing

PointStatic balancingDynamic balancing
Condition satisfiedResultant centrifugal force is zeroResultant force and resultant couple are both zero
MassesCan be in one plane or several planesMasses in different planes
TestShaft placed on rails (knife edges); it stays at rest in any positionNeeds a balancing machine with the shaft rotating
Planes neededOne correcting mass in one planeAt least two correcting planes
Remaining defectA couple may remainNo residual force or couple
Suitable forNarrow discs and wheelsLong rotors, crankshafts, armatures

Dynamic balance includes static balance, but static balance does not guarantee dynamic balance.

Conditions for complete balance (several masses in different planes)

  1. The vector sum of all the centrifugal forces is zero:
∑mrω2=0  ⇒  ∑mr=0\sum mr\omega^2 = 0 \;\Rightarrow\; \sum mr = 0
  1. The vector sum of the couples about any reference plane is zero:
∑mr l=0\sum mr\,l = 0

where ll is the axial distance of each plane from the reference plane. Both conditions are solved graphically (force and couple polygons) or by resolving into horizontal and vertical components.

✓ Answer checked by Claude Opus 5.5 (high effort)

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