Dynamic Balancing Machine Experiment: Procedure, Theory, and Vector Diagram Method

Aim: To determine the unbalanced masses and their angular positions in a rotating shaft system, and to achieve complete dynamic balancing by adding or removing correction masses.

Apparatus Required

• Dynamic Balancing Machine with shaft, removable mass discs, and angular position scale
• Variable-speed motor drive
• Tachometer / stroboscope
• Set of balancing masses (known weights)

Theory

Static balance: A rotor is statically balanced if its centre of mass lies on the axis of rotation — the resultant centrifugal force is zero: Σmrω² = 0, i.e., Σmr = 0. Dynamic balance: A rotor is dynamically balanced if both the resultant centrifugal force AND the resultant couple are zero: Σmr = 0 and Σmrl = 0 (where l is the axial distance from a reference plane).

A rotor can be statically balanced but dynamically unbalanced — this causes vibration at running speed. Complete dynamic balance requires two correction planes.

Procedure

1. Mount the unbalanced mass discs (given masses at specified angles and axial positions) on the shaft.
2. Draw the couple polygon: select a reference plane; calculate mr × l for each mass. Plot these vectors graphically — the closing vector gives the couple to be balanced in a chosen correction plane.
3. Draw the force polygon: after fixing the couple in one plane, plot mr vectors. The closing vector gives the force to be balanced in the second correction plane.
4. Add the calculated correction masses at the determined angles and axial positions.
5. Run the machine and verify smooth operation (no vibration at test speed). Check with stroboscope that no oscillation is visible.

Calculations — Analytical Method

Taking a reference plane (RP) between the two balance planes:
Step 1 — Couple polygon: Resolve each mr·l vector into x and y components. Sum = 0 gives the correction couple (mB·rB·lB).
Step 2 — Force polygon: Resolve each mr vector including the couple correction mass. Sum = 0 gives the correction force (mC·rC).
Angle of correction mass: θ = arctan(ΣmrSinθ / ΣmrCosθ) + 180° (opposite direction to close polygon)

Frequently Asked Questions

What is the difference between static and dynamic balancing?
Static balance means the centre of mass of the rotor lies on the rotation axis — no net centrifugal force. Dynamic balance additionally requires no net unbalanced couple — meaning all centrifugal forces produce no net moment about any plane perpendicular to the shaft. A statically balanced rotor can still be dynamically unbalanced (causing vibration during rotation).

How many balancing planes are needed for dynamic balancing?
Dynamic balancing always requires correction in exactly two planes. This is because dynamic imbalance is characterised by two independent quantities — the magnitude and angle of the correction in each of two planes. Static balancing can be achieved in a single plane.

What happens if a rotating machine is not dynamically balanced?
An unbalanced rotating machine causes vibration at rotational frequency — leading to bearing wear, structural fatigue, noise, and reduced machinery life. High-speed rotors (turbines, motors, fans) require precision dynamic balancing to ISO 1940-1 grade G2.5 or better to prevent premature failure.

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