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Spindle Speed Formula

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Spindle Speed is the speed of machine tool spindle given in revolutions per minute. Check FAQs

N = V cutting \cdot \frac{1000}{π \cdot D t}

N - Spindle Speed?V_cutting - Cutting Speed?D_t - Diameter of Cutting Tool?π - Archimedes' constant?

Spindle Speed Example

With values

With units

Only example

Here is how the Spindle Speed equation looks like with Values.

Here is how the Spindle Speed equation looks like with Units.

Here is how the Spindle Speed equation looks like.

28308.3592 = 66.7 \cdot \frac{1000}{3.1416 \cdot 45}

28308.3592rev/min = 66.7m/s \cdot \frac{1000}{3.1416 \cdot 45mm}

28308.3592 = 66.7 \cdot \frac{1000}{3.1416 \cdot 45}

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Spindle Speed Solution

Follow our step by step solution on how to calculate Spindle Speed?

FIRST Step Consider the formula

N = V cutting \cdot \frac{1000}{π \cdot D t}

Next Step Substitute values of Variables

∴

N = 66.7m/s \cdot \frac{1000}{π \cdot 45mm}

Next Step Substitute values of Constants

∴

N = 66.7m/s \cdot \frac{1000}{3.1416 \cdot 45mm}

Next Step Convert Units

∴

N = 4002m/min \cdot \frac{1000}{3.1416 \cdot 45mm}

Next Step Prepare to Evaluate

∴

N = 4002 \cdot \frac{1000}{3.1416 \cdot 45}

Next Step Evaluate

∴

N = 2964.44444429349rad/s

Next Step Convert to Output's Unit

∴

N = 28308.3592112784rev/min

LAST Step Rounding Answer

∴

N = 28308.3592rev/min

Spindle Speed Formula Elements

Variables

Constants

Spindle Speed

Spindle Speed is the speed of machine tool spindle given in revolutions per minute.

Symbol: N

Measurement: Angular VelocityUnit: rev/min

Note: Value can be positive or negative.

Formulas to find Spindle Speed

Cutting Speed

Cutting Speed is defined as the speed at which the work moves with respect to the tool (usually measured in feet per minute).

Symbol: V_cutting

Measurement: SpeedUnit: m/s

Note: Value can be positive or negative.

Formulas to find Cutting Speed

Diameter of Cutting Tool

The Diameter of Cutting Tool is the outer diameter of the cutting part of the tool.

Symbol: D_t

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Diameter of Cutting Tool

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

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How to Evaluate Spindle Speed?

Spindle Speed evaluator uses Spindle Speed = Cutting Speed*1000/(pi*Diameter of Cutting Tool) to evaluate the Spindle Speed, The Spindle speed is the speed at which the cutting tool rotates, it is tool speed. Spindle Speed is denoted by N symbol.

How to evaluate Spindle Speed using this online evaluator? To use this online evaluator for Spindle Speed, enter Cutting Speed (V_cutting) & Diameter of Cutting Tool (D_t) and hit the calculate button.

FAQs on Spindle Speed

What is the formula to find Spindle Speed?

The formula of Spindle Speed is expressed as Spindle Speed = Cutting Speed*1000/(pi*Diameter of Cutting Tool). Here is an example- 270324.9 = 66.7*1000/(pi*0.045).

How to calculate Spindle Speed?

With Cutting Speed (V_cutting) & Diameter of Cutting Tool (D_t) we can find Spindle Speed using the formula - Spindle Speed = Cutting Speed*1000/(pi*Diameter of Cutting Tool). This formula also uses Archimedes' constant .

Can the Spindle Speed be negative?

Yes, the Spindle Speed, measured in Angular Velocity can be negative.

Which unit is used to measure Spindle Speed?

Spindle Speed is usually measured using the Revolution per Minute[rev/min] for Angular Velocity. Radian per Second[rev/min], Radian per Day[rev/min], Radian per Hour[rev/min] are the few other units in which Spindle Speed can be measured.

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