Essential Formulas for Calculating Drilling Parameters

When it comes to precision and efficiency in manufacturing, few processes are as foundational—or as critical—as drilling. Whether you’re a seasoned engineer or a student entering the world of mechanical or industrial engineering, understanding how to correctly calculate drilling parameters can significantly impact the quality of your work, the lifespan of your equipment, and the overall productivity of your operations.

This guide demystifies the essential formulas used in drilling calculations, providing you with practical tools to determine cutting speeds, spindle speeds, feed rates, and material removal rates. Armed with these formulas, you’ll be able to make more informed decisions on the shop floor or in academic assessments, ensuring optimal performance across a range of applications.

The below collection of equations can be used to calculate specific parameters during turning, drilling, and milling. Knowing the correct speeds, feeds, and depths of cut are critical for successful drilling.

Knowing cutting forces is important to ensure you select the correct type of tool for the job, such as the material of the tool (HSS vs solid carbide for example), and the safe amount of material you can remove at each pass without risk to the workpiece or the cutter.

All calculations below are assuming metric sizing; however the format of the equations can be also used for imperial sizes with the correct translation from metric to imperial. 

Cutting speed (V_C), m/min 

V_c = ^{D_c x π x n} / ₁₀₀₀

Where D_C = Diameter of the cutter in mm, and n = spindle speed in RPM

Spindle Speed (n), RPM (revs per minute)

n = ^{V_c x 1000} / _{π x Dc}

Where D_C = Diameter of the cutter in mm, V_C = cutter speed

Penetration Rate (V_f)  mm/min

This formula is used to link the below two parameters:

Penetration rate (V_f)  – (longitudinal speed at which the drill is cutting into the material) 

Feed per Revolution’ (f_n) – the depth of material cut for each full revolution of the drill.

V_f = f_n x n

where n = spindle speed, f_n = Feed per revolution (mm/rev)

 

Material Removal Rate (Q), cm³/min

Q = ^{D_c x f_n x V_c} / ₄

Machining Time (T_C), min

T_c = ^L_m / _Vf

Where L_m = length of material to be drilling (m)

Net Power (P_c) kW

P_c = ^{f_n x V_c x D_c x K_c} / _240×10³

where K_C = Specific Cutting force. (This is defined as the force needed to cut a chip area of 1 mm² that has a thickness of 1 mm).

Example K_C values are given below:

Torque (M_C), Nm​

M_c = ^{P_c x 30 x103} / _{π x n}

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Example Drilling Calculation

Calculate:

i) The appropriate spindle speed

ii) material removal rate

iii) total machining time to drill 120 holes (assume 10 seconds set-up per hole)

iv) net power consumption

v) drilling torque required…

…for a 12mm HSS drill, drilling through 80 mm thick aluminium alloy.  Take the appropriate cutting speed for the material to be 60m/min, feed per revolution to be 0.1mm/rev and specific cutting force required to be 690N/mm².

i) Spindle speed, n:

n = ^{V_c x 1000} / _{π x Dc}

n = ^{60 x 1000} / _{π x 12}

n = 1592 RPM

ii) material removal rate, Q:

Q = ^{D_c x f_n x V_c} / ₄

Q = ^{12 x 0.1 x 60} / ₄

Q = 18.0cm³/min

iii) Total machining time, T_C

T_c = ^L_m / _Vf

V_f = f_n x n = 0.1 x 1592 = 159.2 mm/ min

T_c = ⁸⁰ / _159.2 = 0.5 min per hole

Therefore for 120hole = 0.5 x 120 = 60mins 

+ setup time of 10 seconds per hole = 120 x 10 = 1200 seconds = 20 mins

Total time = 60+20 = 80minutes

iv) net power consumption

P_c = ^{f_n x V_c x D_c x K_c} / _240×10³

P_c = ^{0.1 x 60 x 12 x 690} / _{240 x 10³}

P_c = 0.207kW

v) torque required

M_c = ^{P_c x 30 x103} / _{π x n}

Mc = ^{0.207 x 30×103} /  _{π x 1592} 

Mc = 1.24Nm

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