Balancing of Machines – ECET 2026 Mechanical Theory of Machines Complete Notes

Concept Notes (Deep Explanation + Examples)

🔹 Introduction

In any rotating or reciprocating machine — like an engine, compressor, or turbine — unbalanced forces cause vibrations, noise, wear, and mechanical failure.
The process of eliminating or reducing these unbalanced forces is called Balancing of Machines.

Balancing ensures smooth running, less vibration, and longer life of machines.

🔹 Why Balancing is Important

Prevents excessive vibrations that may damage bearings and foundations.
Reduces power loss due to dynamic forces.
Increases speed limits safely.
Improves operator comfort and accuracy in instruments like gyroscopes or turbines.

🔹 Types of Balancing

1️⃣ Static Balancing
2️⃣ Dynamic Balancing

Let’s understand both.

🔸 Static Balancing

When the centre of gravity (C.G.) of a system of masses lies on the axis of rotation, the system is statically balanced.

👉 Example:
A grinding wheel mounted on a shaft should not rotate by itself when placed horizontally — if it does, it’s unbalanced.

📖 Condition for static balance:
The vector sum of all centrifugal forces (or their masses × radius) must be zero.

$\sum m_i r_i = 0$

🔸 Dynamic Balancing

When a body rotates, forces not only act in one plane but in multiple planes along the shaft.

A system is dynamically balanced when no resultant centrifugal force or couple acts on the system.

📖 Condition for dynamic balance:
Both:
$\sum m_i r_i = 0 \quad \text{and} \quad \sum m_i r_i l_i = 0$
where $l_i$ = distance between planes of rotation.

🔹 Balancing of Rotating Masses

A rotating mass produces centrifugal force on the shaft.

$F = m \omega^2 r$

where:

$m$ = mass of rotating body (kg)
$\omega$ = angular speed (rad/s)
$r$ = radius of rotation (m)

To balance a rotating mass, another mass is added in the opposite direction to neutralize the force.

Example (Practical Workshop Case):

A rotor with a heavy spot vibrates when spun. To balance, we attach a counterweight opposite the heavy side.
This ensures the rotor runs smoothly even at high RPM.

🔹 Balancing of Several Masses in the Same Plane

If several masses rotate in the same plane:

Draw the vector diagram of $m_i r_i$ for all masses (using scale).
The closing side of the polygon gives the required balancing mass in magnitude and direction.

🔹 Balancing of Several Masses in Different Planes

For masses rotating in different planes:

Find the resultant force polygon (for magnitudes).
Find the couple polygon (for moment arms).
The balancing mass is located and adjusted to close both polygons simultaneously.

🔹 Balancing of Reciprocating Masses

In reciprocating engines, pistons move back and forth.
Their motion causes primary and secondary unbalanced forces.

Primary Force:

$F_p = m r \omega^2 \cos \theta$

Secondary Force:

$F_s = m r \omega^2 \frac{r}{l} \cos 2\theta$

where:

$l$ = length of connecting rod
$\theta$ = crank angle

Usually, only partial balancing is done in reciprocating engines (around 50–60%) because perfect balancing increases other stresses.

🔹 Practical Applications

Car engines – To reduce vibration from pistons.
Turbines & Flywheels – For smooth power transmission.
Fans & Rotors – To avoid noise and damage.
Crankshafts – Balanced dynamically for long life.

⚙️ Formulas (Plain LaTeX)

$F = m \omega^2 r$
$\sum m_i r_i = 0$
$\sum m_i r_i l_i = 0$
$F_p = m r \omega^2 \cos \theta$
$F_s = m r \omega^2 \frac{r}{l} \cos 2\theta$
$\text{Balancing Mass, } m_b = \frac{m_1 r_1}{r_b}$
$\omega = 2 \pi N / 60$
$\text{Couple, } C = m r \omega^2 l$
$\text{Resultant Force} = \sqrt{(\sum F_x)^2 + (\sum F_y)^2}$

$\text{Resultant Couple} = \sqrt{(\sum C_x)^2 + (\sum C_y)^2}$

🔟 10 MCQs (GATE + ECET Mix)

Balancing of machines is done to eliminate:
A) Pressure loss
B) Vibration and noise
C) Power transmission
D) Lubrication problems
Static balancing requires:
A) Resultant couple = 0
B) Resultant force = 0
C) Both force and couple = 0
D) Centrifugal force = Maximum
Dynamic balancing ensures:
A) No resultant couple and no resultant force
B) Resultant force only zero
C) Resultant couple only zero
D) None of these
Centrifugal force on a rotating mass is proportional to:
A) r
B) $r^2$
C) $\omega^2 r$
D) $\omega r^2$
Primary unbalanced force in reciprocating engine is:
A) $m r \omega^2 \sin \theta$
B) $m r \omega^2 \cos \theta$
C) $m r^2 \omega \cos \theta$
D) $m \omega^2 r^2 \sin \theta$
For dynamic balancing, the conditions are:
A) $\sum m r = 0$ and $\sum m r l = 0$
B) $\sum F = 0$ only
C) $\sum C = 0$ only
D) $\sum \theta = 0$
In a single-cylinder reciprocating engine, only ______ balancing is possible.
A) Static
B) Dynamic
C) Partial
D) Complete
Unbalanced forces cause:
A) Uniform motion
B) Vibrations
C) Power increase
D) Temperature rise only
The couple due to rotating mass is:
A) $m r \omega^2 l$
B) $m r^2 \omega l$
C) $m l^2 \omega r$
D) $m r \omega^2 / l$
In practice, reciprocating engines are:
A) Completely balanced
B) 50–60% balanced
C) 25% balanced
D) Not balanced

✅ Answer Key

Q.No Answer
1 B
2 B
3 A
4 C
5 B
6 A
7 C
8 B
9 A
10 B

🧠 MCQ Explanations

1️⃣ B: Balancing reduces vibration and noise. Other options unrelated to balance.
2️⃣ B: Static balance → resultant centrifugal force = 0.
3️⃣ A: Dynamic balance → no resultant force and no couple.
4️⃣ C: $F = m \omega^2 r$ , proportional to $\omega^2 r$ .
5️⃣ B: Primary unbalanced force = $m r \omega^2 \cos \theta$ .
6️⃣ A: Both force and couple must be zero for dynamic balance.
7️⃣ C: Reciprocating engines can’t be fully balanced → only partial.
8️⃣ B: Unbalanced forces cause vibration.
9️⃣ A: Couple = $m r \omega^2 l$ .
10️⃣ B: Practical balancing is around 50–60% to reduce secondary forces.

🎯 Motivation (ECET 2026 Specific)

Balancing questions appear every year in ECET because they combine theory + simple math.
If you master this topic, you’ll easily secure 2–3 marks in Theory of Machines.
Practicing such concepts regularly helps you visualize motion, improve mechanical intuition, and boost rank stability.
Consistency is the secret — one topic daily = top performance in ECET 2026!

📲 CTA

Join our ECET 2026 Mechanical WhatsApp Group for daily quizzes & study notes:
👉 https://chat.whatsapp.com/GniYuv3CYVDKjPWEN086X9

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Balancing of Machines – ECET 2026 Theory of Machines Complete Notes

Concept Notes (Deep Explanation + Examples)

🔹 Introduction

🔹 Why Balancing is Important

🔹 Types of Balancing

🔸 Static Balancing

🔸 Dynamic Balancing

🔹 Balancing of Rotating Masses

Example (Practical Workshop Case):

🔹 Balancing of Several Masses in the Same Plane

🔹 Balancing of Several Masses in Different Planes

🔹 Balancing of Reciprocating Masses

Primary Force:

Secondary Force:

🔹 Practical Applications

⚙️ Formulas (Plain LaTeX)

🔟 10 MCQs (GATE + ECET Mix)

✅ Answer Key

🧠 MCQ Explanations

🎯 Motivation (ECET 2026 Specific)

📲 CTA

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CONTACTS

Balancing of Machines – ECET 2026 Theory of Machines Complete Notes

Concept Notes (Deep Explanation + Examples)

🔹 Introduction

🔹 Why Balancing is Important

🔹 Types of Balancing

🔸 Static Balancing

🔸 Dynamic Balancing

🔹 Balancing of Rotating Masses

Example (Practical Workshop Case):

🔹 Balancing of Several Masses in the Same Plane

🔹 Balancing of Several Masses in Different Planes

🔹 Balancing of Reciprocating Masses

Primary Force:

Secondary Force:

🔹 Practical Applications

⚙️ Formulas (Plain LaTeX)

🔟 10 MCQs (GATE + ECET Mix)

✅ Answer Key

🧠 MCQ Explanations

🎯 Motivation (ECET 2026 Specific)

📲 CTA

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Important Links

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