Balancing of Rotating Masses — Static and Dynamic Balancing Experiment Procedure

The balancing of rotating masses is a critical topic in Theory of Machines and Design of Machine Elements. Unbalanced rotating masses cause vibrations, bearing loads, and fatigue failures in rotating equipment including turbines, compressors, crankshafts, and propeller shafts. This experiment teaches students to identify and correct imbalance using both graphical and analytical methods.

Aim of the Experiment

1. To understand the concept of static and dynamic balancing.
2. To balance a given system of rotating masses using the graphical polygon method and verify using the experimental apparatus.

Theory

Static Balancing

A system of rotating masses is said to be in static balance when the resultant centrifugal force acting on the shaft is zero. The condition for static balance is:

ΣF = 0 → Σmrω² = 0 → Σmr = 0 (since ω² is common)

Graphically, this means the force polygon closes — the vectors m₁r₁, m₂r₂, m₃r₃ drawn tip-to-tail form a closed polygon.

Dynamic Balancing

Static balance only ensures no net force. For dynamic balance, there must also be no net couple (moment) about any plane:

ΣM = 0 → Σmrω²l = 0 → Σmrl = 0

where l = distance of each mass from a reference plane.

A system is dynamically balanced only when BOTH the force polygon AND the couple polygon close.

Balancing Procedure — Graphical Method

1. Choose a reference plane (typically the plane of mass 1)
2. Draw the couple polygon using mrl vectors — this gives the position and magnitude of the balancing couple mass
3. Draw the force polygon using mr vectors — this gives the balancing force mass position and magnitude

Apparatus Required

• Dynamic balancing machine (motorised rotating shaft with adjustable mass holders)
• Disc masses of known mass (m₁, m₂, m₃, m₄) at different radii
• Protractor for angular positioning
• Ruler, drawing board, pencil for graphical polygon
• Stroboscope (for checking residual imbalance visually)
• Vibration indicator (optional)

Procedure

1. Setup: Mount three masses (m₁, m₂, m₃) at their given radii (r₁, r₂, r₃) and angular positions (θ₁, θ₂, θ₃) on the rotating shaft. Record all values.
2. Couple polygon: Select a reference plane (Plane 1). Calculate mrl for each mass. Draw the couple polygon to scale. The closing vector gives the magnitude and direction of the balancing mass in its plane (Plane 4).
3. Force polygon: Calculate mr for each mass including the balancing couple mass from Step 2. Draw the force polygon. The closing vector gives the balancing force mass magnitude and direction.
4. Apply balancing masses: Mount the calculated balancing masses at the positions determined graphically.
5. Verification: Run the apparatus and observe vibration. A balanced shaft will run smoothly; residual vibration indicates calculation or mounting error.
6. Repeat with a different configuration of masses as specified by the instructor.

Sample Problem

Four masses A, B, C, D are completely balanced. Masses B, C, D are 50 kg, 80 kg, and 70 kg respectively. The planes containing masses B and C are 300 mm apart. The planes containing A and B are 400 mm apart, and planes containing C and D are 600 mm apart. The eccentricities of B, C, D are 150 mm, 200 mm, and 100 mm respectively. Find the mass A, eccentricity of A, and angular positions of all masses.

Solution Approach

• Set up the couple polygon using mrl values with plane A as reference
• Draw couple polygon: mrBIB, mrClc, mrDlD
• Close the polygon to find mrAlA
• Set up force polygon using mr values
• Close to find mrA
• Calculate mass A and its eccentricity

Observation Table

Results

• Balancing mass required in Plane A = _____ kg
• Eccentricity of mass A = _____ mm
• Angular position of mass A = _____ degrees
• After applying balancing masses, the shaft ran with negligible vibration — dynamic balance achieved.

Viva Questions

1. What is the difference between static and dynamic balancing?
2. Can a system be statically balanced but dynamically unbalanced? Give an example.
3. Why is dynamic balancing more important than static balancing for high-speed machinery?
4. What happens if a crankshaft is not properly balanced?
5. Explain the graphical method of balancing rotating masses.
6. What is a balancing machine? How does it work?
7. Why are tyres of vehicles balanced? What symptoms indicate wheel imbalance?

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