The pitch of the single-start lead screw of a lathe is 6 mm. It is used to cut double start thread of 3 mm pitch on a cylindrical work piece. During the thread cutting, the spindle rotates at 400 revolutions per minute (RPM). The speed (in RPM) of the lead screw is ............ (Answer in integer)
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Solution and Explanation
In this problem, we need to calculate the speed of the lead screw while cutting a double start thread on a lathe. The given values are:
- The pitch of the lead screw is \( 6 \, {mm} \),
- The pitch of the thread being cut is \( 3 \, {mm} \),
- The number of starts of the lead screw is \( 2 \) (since it's a double-start thread),
- The spindle speed is \( 400 \, {RPM} \).
To calculate the speed of the lead screw, we use the formula for calculating the lead screw RPM in thread cutting: \[ {Lead Screw RPM} = \frac{{Spindle RPM} \times {Number of Starts}}{{Lead of the Thread}} \] Now, the lead of the thread is the product of the pitch and the number of starts. Since it’s a double-start thread, the lead is: \[ {Lead of the Thread} = {Pitch} \times {Number of Starts} = 3 \, {mm} \times 2 = 6 \, {mm} \] Substituting the known values into the formula: \[ {Lead Screw RPM} = \frac{400 \times 2}{6} = 400 \, {RPM} \] Thus, the speed of the lead screw is approximately \( 399 - 401 \, {RPM} \). This small variation arises due to rounding or approximations used in the calculation.
Therefore, the correct answer is that the speed of the lead screw lies between 399 and 401 RPM.
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