Calculation of Gear Ratios for Metric Thread Cutting on Inch Lead Screw Lathe and Vice-Versa

In the ITI Turner trade, lathes are commonly equipped with either metric or inch lead screws. When a thread of one system is to be cut on a lathe of another system, special gear ratio calculations are required. This chapter explains the calculation of gear ratios for cutting metric threads on an inch lead screw lathe and inch threads on a metric lead screw lathe.

Introduction

The lead screw of a lathe controls the movement of the cutting tool. Its pitch determines how far the tool moves per revolution of the spindle. For correct thread cutting, the movement of the tool must match the required thread pitch.

Basic Principle

Gear Ratio = Lead Screw Pitch / Thread Pitch

However, when units differ (metric vs inch), a conversion factor is required.

Metric to Inch Conversion

1 inch = 25.4 mm

Case 1: Cutting Metric Threads on Inch Lead Screw Lathe

Formula

Gear Ratio = (Lead Screw Pitch × 25.4) / Metric Pitch

Example

Lead screw pitch = 4 TPI (Threads per inch)
Required metric pitch = 2 mm

Lead screw pitch in mm = 25.4 / 4 = 6.35 mm

Gear ratio = 6.35 / 2 = 3.175

This ratio is achieved using a transposing gear (127 teeth).

Use of 127 Gear

The gear with 127 teeth is used because:

127 / 5 = 25.4

It provides exact conversion between inch and metric systems.

Case 2: Cutting Inch Threads on Metric Lead Screw Lathe

Formula

Gear Ratio = (Lead Screw Pitch in mm) / (TPI × 25.4)

Example

Lead screw pitch = 6 mm
Required thread = 8 TPI

Thread pitch in mm = 25.4 / 8 = 3.175 mm

Gear ratio = 6 / 3.175 ≈ 1.89

This is achieved using suitable gear combinations with a 127 gear.

Transposing Gears

Transposing gears are used to convert between inch and metric systems. The most common gear used is 127 teeth gear.

Arrangement

• 127 gear combined with 100 gear
• Placed in gear train to achieve conversion

Simple Gear Train Calculation

Gear Ratio = Driven / Driver

Compound Gear Train Calculation

Gear Ratio = (Driven1 × Driven2) / (Driver1 × Driver2)

Importance of Accurate Calculation

• Ensures correct thread pitch
• Prevents mismatch of threads
• Improves machining accuracy

Precautions

• Use correct conversion factor
• Ensure proper gear alignment
• Check gear teeth carefully

Application in Turner Workshop

In the Turner trade, these calculations are used when different thread systems are required. Operators use transposing gears to achieve accurate conversion between metric and inch systems.

Proper setup ensures correct thread cutting.

Advantages

• Allows versatility in thread cutting
• Enables use of single lathe for different systems
• Improves efficiency

Conclusion

Calculation of gear ratios for metric and inch thread cutting is essential in the ITI Turner trade. Proper use of conversion factors and transposing gears ensures accurate thread production.

Understanding these calculations helps in achieving precision and efficiency.

In conclusion, mastering these concepts is crucial for advanced thread cutting operations.