Lesson 4.4: Design of Bearings, Springs, Brakes & Clutches

Machine elements like bearings, springs, brakes, and clutches are essential for smooth operation, load support, and motion control. GATE and PSU exams frequently test design calculations, load capacity, and selection criteria.

🔹 1. Bearings

• Definition: Bearings support rotating shafts and reduce friction between moving parts.

• Types:

  1. Ball Bearings → low load, high speed

  2. Roller Bearings → moderate load, moderate speed

  3. Journal Bearings / Sleeve Bearings → high load, low speed

• Design Considerations:

  • Radial and axial load capacity

  • Bearing life: L10=CP3∗106L_{10} = \frac{C}{P}^3 * 10^6L10​=PC​3∗106 revolutions (for ball/roller bearings)

  • Lubrication and material selection

🔹 2. Springs

• Purpose: Store and release energy, absorb shock, maintain force.

• Types:

  1. Helical (Compression/Tension) Springs

  2. Torsion Springs

  3. Leaf Springs

• Design Considerations:

  • Maximum stress (shear for helical spring):

τmax⁡=8WDπd3K\tau_{\max} = \frac{8 W D}{\pi d^3} Kτmax​=πd38WD​K

Where W = load, D = mean coil diameter, d = wire diameter, K = Wahl factor

• Example: Helical spring carrying 500 N, mean diameter 50 mm, wire diameter 10 mm → calculate stress and deflection

🔹 3. Brakes

• Purpose: Slow down or stop motion by friction.

• Types:

  1. Drum Brake → internal/external shoe

  2. Disc Brake → high-speed, effective cooling

  3. Band Brake → used in small machines

• Design Considerations:

  • Braking torque: $T=Fr$

  • Friction material selection

  • Heat dissipation during braking

• Example: Design a drum brake to stop 500 kg rotating mass with 0.5 m radius, coefficient of friction 0.3

🔹 4. Clutches

• Purpose: Transmit torque intermittently between shafts.

• Types:

  1. Friction Clutch → single plate, multi-plate

  2. Positive Clutch → gear, dog type

• Design Considerations:

  • Torque transmission capacity: $T=\mu Fr$

  • Plate diameter, number of friction surfaces

  • Engagement force, factor of safety

• Example: Single plate clutch transmitting 20 kW at 1000 rpm, coefficient of friction 0.25 → calculate required plate diameter and axial force

🔹 5. Solved Examples (PYQ Style)

Example 1 (GATE ME 2018):
Design a helical compression spring for load 500 N, mean diameter 50 mm, wire diameter 10 mm, allowable shear stress 500 MPa.

Example 2 (PSU Exam):
Design single plate friction clutch transmitting 15 kW at 1200 rpm, coefficient of friction 0.3. Find plate diameter and axial load.

Example 3:
Select a ball bearing for shaft subjected to radial load 2 kN, axial load 0.5 kN, desired life 10,000 hours at 1000 rpm.

🔹 6. Practice Exercises

1. Calculate maximum stress and deflection in a helical spring under given load.

2. Determine braking torque for drum and disc brakes.

3. Design clutch plate diameter and axial force for given torque.

4. Select bearing type and calculate bearing life for specified loads.

5. Compare design considerations of friction vs positive clutches.

🔹 7. Summary

• Bearings: Support shafts, reduce friction, consider radial/axial load and life

• Springs: Store energy, absorb shock, shear/torsion stress critical

• Brakes: Provide stopping torque, friction and heat dissipation important

• Clutches: Transmit torque intermittently, friction, plate size, axial load key