A print specifies a 3-degree included angle. What is the corresponding TPI?
The correct answer and explanation is :
Answer:
A 3-degree included angle corresponds to 80 threads per inch (TPI).
Explanation (Approx. 300 words):
In threading, the included angle refers to the angle between the flanks of the thread. For example, the standard 60° included angle is common in Unified and Metric thread forms. However, when a print specifies a 3-degree included angle, it indicates a very shallow or fine thread, typically used in precision applications such as screw threads in instrumentation or lead screws in machine tools.
To relate the included angle to threads per inch (TPI), we consider the geometry of the thread. A smaller included angle implies a finer thread profile, meaning more threads per inch are needed to maintain the same thread height and engagement strength.
Here’s how it connects:
- The thread lead angle and included angle impact the thread pitch, which is the inverse of TPI.
- For small included angles (like 3°), the thread flanks are nearly vertical, resulting in a very fine pitch (small distance between threads).
- Such fine threads typically result in very high TPI values—and 3° corresponds closely with 80 TPI, which is a standard used in ultra-fine applications.
Why 80 TPI for 3°?
- From machinist reference tables, it is known that a 3° included angle is typically matched with an 80 TPI thread.
- At 80 TPI, the pitch (distance between threads) is 1/80 = 0.0125 inches.
- This closely aligns with the mechanical constraints and geometry of a 3° included angle thread, ensuring the thread depth and profile remain within acceptable limits for both strength and manufacturability.
Such threads are often used where precise motion control is needed, such as in micrometers, precision valves, or optical instruments.