Design of Gears free study notes for Diploma / BTech.

1. What is Gears ?

Gears are mechanical elements used for transmitting motion and power between rotating shafts with a constant velocity ratio. They are widely used in machines like automobiles, turbines, gearboxes, and industrial equipment due to their high efficiency and reliability.

2. Types of Gears

Based on shaft arrangement, gears are classified as:

(a) Parallel Shaft Gears

• Spur Gears
• Helical Gears
• Double Helical (Herringbone) Gears

(b) Intersecting Shaft Gears

• Bevel Gears (straight, spiral)

(c) Skew Shaft Gears

• Worm and Worm Wheel
• Hypoid Gears

3. Gear Terminology

Important terms used in gear design:

• Pitch Circle: Imaginary circle rolling without slipping
• Pitch Diameter (d): Diameter of pitch circle
• Module (m): Ratio of pitch diameter to number of teeth $$m = \frac{d}{Z}$$
• Circular Pitch (p): Distance between corresponding points on adjacent teeth
• Pressure Angle (φ): Angle between line of action and tangent to pitch circle
• Addendum: Height above pitch circle
• Dedendum: Depth below pitch circle
• Tooth Thickness: Width of tooth at pitch circle

4. Law of Gearing

For smooth power transmission, gears must satisfy the law of gearing:

The common normal at the point of contact between two gear teeth must always pass through a fixed point on the line joining the centers.

This ensures constant velocity ratio.

5. Gear Tooth Profiles

Two main profiles are used:

• Involute Profile (most common)
  • Easy to manufacture
  • Constant velocity ratio even with slight misalignment
• Cycloidal Profile
  • Less commonly used
  • Used in clocks and light mechanisms

6. Material Selection for Gears

Material selection depends on load, speed, and operating conditions.

• Cast Iron – good wear resistance
• Steel (Plain Carbon / Alloy Steel) – high strength
• Bronze – used in worm gears
• Plastics (Nylon, Teflon) – for low load and noise reduction

7. Gear Design Considerations

Key factors in gear design include:

• Strength of teeth
• Wear resistance
• Noise and vibration
• Lubrication
• Manufacturing feasibility
• Alignment and mounting

8. Forces Acting on Gear Teeth

When gears mesh, the following forces act:

• Tangential Force (Ft) – transmits power
• Radial Force (Fr) – tends to separate gears
• Axial Force (Fa) – present in helical gears

9. Gear Tooth Strength (Lewis Equation)

The bending strength of gear teeth is calculated using the Lewis equation:$$F_t = \sigma_b \cdot b \cdot m \cdot Y$$

Where:

• $F_t$Ft​ = Tangential force
• $\sigma_b$σb​ = Allowable bending stress
• $b$b = Face width
• $m$m = Module
• $Y$Y = Lewis form factor

10. Dynamic and Wear Load

(a) Dynamic Load

Accounts for inaccuracies and vibrations using Buckingham equation.

(b) Wear Load

Calculated using:$$F_w = d \cdot b \cdot Q \cdot K$$

Where:

• $Q$Q = Load sharing factor
• $K$K = Material factor

11. Beam Strength vs Wear Strength

• Beam Strength: Resistance to bending failure
• Wear Strength: Resistance to surface failure

Design condition:$$\text{Wear strength} > \text{Beam strength}$$

12. Design Procedure of Spur Gear

Step-by-step approach:

1. Select material for pinion and gear
2. Determine power and speed
3. Calculate tangential load
4. Select module using Lewis equation
5. Check for wear failure
6. Determine face width (b ≈ 10m to 12m)
7. Calculate dimensions (pitch diameter, etc.)
8. Check dynamic load
9. Provide lubrication system

13. Gear Failures

Common types of gear failures:

• Tooth Breakage (bending failure)
• Pitting (surface fatigue)
• Scoring (due to lubrication failure)
• Wear (abrasive/corrosive)

14. Advantages of Gears

• High efficiency (up to 99%)
• Positive drive (no slip)
• Compact and reliable
• Wide range of speed ratios

15. Disadvantages of Gears

• Costly manufacturing
• Requires precise alignment
• Noisy at high speeds (especially spur gears)

16. Applications of Gears

• Automobiles (gearboxes, differentials)
• Industrial machinery
• Aircraft engines
• Marine drives
• Robotics and automation

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