Calculating the cycle time of Facing, Paring Off and Deep Grooving operations is tricky because:

• The spindle speed is constantly changing.
• At some point during the process, the machine’s maximum RPM limits the cutting speed.

## Facing, Parting Off & Deep Grooving Cycle Time Formulas

• d1 – Starting Diameter
• d2 – End Diameter
• nmax – Machine’s maximum RPM.
• Vc Cutting Speed
• fFeedrate
• dc – Clamped Diameter: The diameter at which the machine’s maximum spindle speed limits the cutting speed (see below)
• t1 Cycle time above the clamped diameter.
• t2 – Cycle time below the clamped diameter.
• T – Total cycle time

Units:

• Times in minutes.
• Diameters in inches or millimeters.
• Cutting speed in SFM of meters/minute.
• Feedrate in IPR or millimeters per revolution

Calculating the operation time of longitudinal turning is straightforward since the diameter is constant. Therefore, the cutting and spindle speeds also remain constant during the whole operation, and the below simple formula applies. (Where l is the distance to turn)

$$\large T = \Large \frac{l}{f \times n}$$

In Facing, Parting Off, and Grooving, the diameter constantly changes, and the total cutting time should be calculated by an integral.

$$\large t_1 = \Large \int_{d_1}^{d_2} \large T(d) = \pi \times \Large \frac{d_1^2\,-\,d_2^2}{12 \times f \times V_c }$$
• In metric units, the constant 12 should be replaced by 1,000

The situation becomes more complicated because each machine has a maximum spindle speed limitation (nmax). To maintain the cutting speed (Vc), the spindle speed (n) increases as the machine moves from d1 to d2.

$$\large n = \Large \frac{12 \times V_c}{\pi \times d}$$
• In metric units, the constant 12 should be replaced by 1,000

At a certain diameter along the way, n will reach nmax. This diameter is called the “Clamped Diameter” (dc) since from this diameter onwards, the spindle speed is “clamped”, and the cutting speed starts to decrease.

$$\large d_c = \Large \frac{12 \times V_c}{\pi \times n_{max}}$$
• In metric units, the constant 12 should be replaced by 1,000

The first formula for t1 is valid only for larger diameters than the clamped diameter. A different and more simple formula is applied for diameters smaller than the clamped diameter.

$$\large t_2 = \Large \frac{d_1\,-\,\,d_2}{2\,\times\,f\,\times\,n_{max}}$$

Summary

To make the correct calculation, you need to identify your situation relative to the clamped diameter.

• Case 1: Both the start and end diameters are larger than the clamped diameter.
• Case 2: The clamped diameter is in between the start and end diameters.
• Case 3: Both the start and end diameters are smaller than the clamped diameter.

Formulas for Case 1:

$$\large T = t_1 = \Large \pi \times \Large \frac{d_1^2\,-\,\,d_2^2}{12 \times f \times V_c }$$

Formulas for Case 2:

$$\large T = t_1 + t_2 = \Large \pi \times \Large \frac{d_1^2\,-\,\,d_c^2}{12 \times f \times V_c } + \frac{d_c\,-\,\,d_2}{2\,\times\,f\,\times\,n_{max}}$$
$$\begin{array}{l} \large T = t_1 + t_2 = \\ \Large \pi \times \Large \frac{d_1^2\,-\,\,d_c^2}{12 \times f \times V_c } \\ \Large\,+\, \frac{d_c\,-\,\,d_2}{2\,\times\,f\,\times\,n_{max}} \end{array}$$

Formulas for Case 3:

$$\large T = t_2 = \Large \frac{d_1\,-\,\,d_2}{2\,\times\,f\,\times\,n_{max}}$$
• In metric units, the constant 12 should be replaced by 1,000
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