Design of Power Transmission Elements free study notes

1. Introduction

Power transmission elements are machine components used to transfer mechanical power from one part of a system to another. They ensure efficient transmission of motion, torque, and energy with minimal losses.

2. Types of Power Transmission Elements

(b) Chain Drives

• Positive drive (no slip)
• Used for moderate distances

Advantages:

• Constant velocity ratio
• High efficiency

Disadvantages:

• Requires lubrication
• Noisy at high speed

(c) Gear Drives

• Rigid transmission with toothed wheels
• Types:
  • Spur
  • Helical
  • Bevel
  • Worm

Advantages:

• No slip
• High efficiency

Disadvantages:

• Expensive
• Requires precise alignment

(d) Shafts

• Rotating element transmitting torque

(e) Couplings

• Connect two shafts

3. General Design Considerations

• Power to be transmitted
• Speed of operation
• Nature of load (steady, shock, fluctuating)
• Efficiency
• Space and cost constraints
• Maintenance requirements

4. Design of Belt Drives

Velocity Ratio

$$\frac{N_1}{N_2} = \frac{D_2}{D_1}$$

Belt Tension Relation

$$\frac{T_1}{T_2} = e^{\mu \theta}$$

Where:

• $T_1, T_2$​ = tight and slack side tensions
• $\mu$μ = coefficient of friction
• $\theta$θ = angle of contact

Power Transmitted

$$P = (T_1 – T_2) \cdot v$$

5. Design of Chain Drives

• Based on:
  • Chain pitch
  • Number of teeth on sprocket
  • Speed ratio

Velocity Ratio

$$\frac{N_1}{N_2} = \frac{T_2}{T_1}$$

6. Design of Gear Drives

Gear Ratio

$$\text{Gear Ratio} = \frac{T_2}{T_1}$$

Lewis Equation (Beam Strength)

$F_t = \sigma \, b \, y \, \pi m$

Where:

• $F_t$Ft​ = tangential force
• $\sigma$σ = allowable stress
• $b$b = face width
• $m$m = module
• $y$y = Lewis form factor

Wear Strength

• Based on surface durability
• Depends on material hardness

7. Design of Shafts

Torsion Equation

$\frac{T}{J} = \frac{\tau}{R} = \frac{G \theta}{L}$

Where:

• $T$T = torque
• $J$J = polar moment of inertia
• $\tau$τ = shear stress

Combined Loading

• Shaft subjected to:
  • Bending moment
  • Torsion

Equivalent torque method used for design

8. Design of Couplings

• Must transmit torque safely
• Types:
  • Rigid (flange, sleeve)
  • Flexible (bush pin, Oldham)

Torque Transmitted

$$T = \frac{P \cdot 60}{2\pi N}$$

9. Material Selection

• High strength and toughness
• Wear resistance
• Common materials:
  • Steel
  • Cast iron
  • Alloy steel

10. Failure of Transmission Elements

• Fatigue failure
• Wear
• Overloading
• Misalignment
• Lubrication failure

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