Question

Massimo, a machinist, is cutting threads for a bolt on a lathe. He wants the bolt to have 18 threads per inch. If the cutting tool moves parallel to the axis of the would be bolt at a linear velocity of 0.080 in./s, what must the rotational speed of the lathe chuck be to ensure the correct thread density? [Hint: One thread is formed for each complete revolution of the chuck.]

Short answer

The chuck should rotate at 86.4 RPM.

Step-by-step solution

Understand the Problem Statement

Massimo needs to create 18 threads per inch on a bolt. Each complete revolution of the lathe chuck results in one thread. The linear velocity of the cutting tool is 0.080 inches per second. We need to find the rotational speed of the chuck in revolutions per minute (RPM).

Determine Thread Formation

Since one thread is formed per complete revolution, and Massimo needs 18 threads per inch, the chuck must complete 18 revolutions per inch.

Calculate the Time for One Inch Movement

The cutting tool moves at a speed of 0.080 inches per second. Thus, the time it takes to move one inch is calculated by dividing the distance (1 inch) by the speed: \[ \text{Time for 1 inch} = \frac{1}{0.080} \text{ seconds} = 12.5 \text{ seconds.} \]

Compute Revolutions per Second

Given that it takes 12.5 seconds to travel one inch and that 18 threads/revolutions are needed in that distance, calculate revolutions per second as follows: \[ \text{Revolutions per second} = \frac{18 \text{ revolutions}}{12.5 \text{ seconds}} = 1.44 \text{ rev/s.} \]

Convert to Revolutions per Minute (RPM)

To convert revolutions per second to revolutions per minute, multiply by 60: \[ \text{Revolutions per minute (RPM)} = 1.44 \text{ rev/s} \times 60 = 86.4 \text{ RPM.} \]

Key concepts

Understanding Linear Velocity

Linear velocity is how fast something is moving in a straight line. For Massimo, the machinist, it is the speed at which the cutting tool moves parallel to the bolt he is crafting. Specifically, in this scenario, the cutting tool has a linear velocity of 0.080 inches per second.

Linear velocity is crucial in machining as it directly impacts how quickly and precisely threads are cut into the bolt. If the tool moves too slowly, production may be inefficient. If it moves too quickly, there might be errors in thread creation.

• Linear velocity ensures synchronization between the tool's movement and the bolt's rotation.
• It determines the time needed to travel a specified distance, like one inch.
• This velocity is also pivotal in calculating the rotational speed of the lathe, as seen in Massimo's threading task.

Knowing the tool's linear velocity helps in precisely controlling how threads are formed, leading to a more efficient machining process.

Exploring Thread Density

Thread density, often expressed in threads per inch (TPI), is a measure of how tightly spaced the threads are on a bolt or screw. For Massimo, achieving a thread density of 18 threads per inch is key to ensuring the bolt fits properly into its intended mating part.

Thread density is an important specification during the design and selection of bolts and screws. It determines not just the strength and tightness of the bolt but also how well it mates with a corresponding nut or threaded hole.

• A higher thread density means more threads are present in a given length.
• Ensuring the correct thread density helps in preventing mechanical failures like stripping or loosening of threads.
• In machining, accurately achieving the specified thread density ensures parts can be assembled and disassembled efficiently.

Understanding thread density ensures that components of machinery and equipment function as intended, maintaining safety and reliability.

Concept of Revolutions Per Minute (RPM)

Revolutions per minute (RPM) is a unit of measurement for rotational speed, indicating the number of complete turns a rotating object makes in one minute. In Massimo's situation, determining the correct RPM of the lathe chuck is vital for forming the threads accurately.

RPM is a critical measure in machining processes because:

• It directly affects the quality and precision of the threads being cut into the bolt.
• An incorrect RPM setting can result in damaged tools, poor surface finishes, and the need for rework.
• The correct RPM balances speed and accuracy, ensuring efficient cutting while preventing tool wear.

In this exercise, converting revolutions per second to RPM was essential to align the lathe's speed with the thread density and linear velocity requirements, assuring precise thread formation.

The Art of Machining Threads

Machining threads is a delicate process of creating spiral ridges on the exterior of a cylinder or within a hole. For Massimo, precision in this task is accomplished through the proper use of the lathe, linear velocity, and thread density.

Machining threads requires careful coordination between various parameters:

• Proper RPM ensures the lathe rotates at a speed conducive to forming neat, precise threads.
• The linear velocity of the cutting tool must be aligned with the rotational speed to avoid inconsistencies in the threading process.
• Correctly achieved thread density means the threads will fit into their counterpart securely, avoiding any mechanical mishaps.

Understanding the machining process helps machinists create compatible and reliable threaded components, fundamental for structural integrity and mechanical functionality.