FormulaDen.com

Physics Chemistry Math Chemical Engineering Civil Electrical Electronics Electronics and Instrumentation Materials Science Mechanical Production Engineering Financial Health

Rotational Frequency of Spindle given Cutting Speed Formula

GoOptimum Spindle Speed Formula

GoOptimum Spindle Speed given Tool Changing Cost Formula

Fx Copy

LaTeX Copy

Rotational Frequency of Spindle is the speed at which the spindle of a machine tool rotates during machining operations. It is typically measured in revolutions per minute. Check FAQs

ω s = \frac{V}{2 \cdot π \cdot r}

ω_s - Rotational Frequency of Spindle?V - Cutting Velocity?r - Instantaneous Radius for Cut?π - Archimedes' constant?

Rotational Frequency of Spindle given Cutting Speed Example

With values

With units

Only example

Here is how the Rotational Frequency of Spindle given Cutting Speed equation looks like with Values.

Here is how the Rotational Frequency of Spindle given Cutting Speed equation looks like with Units.

Here is how the Rotational Frequency of Spindle given Cutting Speed equation looks like.

600 = \frac{8000}{2 \cdot 3.1416 \cdot 2.1221}

600rev/min = \frac{8000mm/min}{2 \cdot 3.1416 \cdot 2.1221mm}

600 = \frac{8000}{2 \cdot 3.1416 \cdot 2.1221}

Tip: Use pencil ( Pencil

) icon above to edit Input Values and Units.

Calculate

Recalculate

Solution

Copy

Reset

You are here -

Home » Category

Engineering » Category

Production Engineering » Category

Metal Machining » fx Rotational Frequency of Spindle given Cutting Speed

Rotational Frequency of Spindle given Cutting Speed Solution

Follow our step by step solution on how to calculate Rotational Frequency of Spindle given Cutting Speed?

FIRST Step Consider the formula

ω s = \frac{V}{2 \cdot π \cdot r}

Next Step Substitute values of Variables

∴

ω s = \frac{8000mm/min}{2 \cdot π \cdot 2.1221mm}

Next Step Substitute values of Constants

∴

ω s = \frac{8000mm/min}{2 \cdot 3.1416 \cdot 2.1221mm}

Next Step Convert Units

∴

ω s = \frac{0.1333m/s}{2 \cdot 3.1416 \cdot 0.0021m}

Next Step Prepare to Evaluate

∴

ω s = \frac{0.1333}{2 \cdot 3.1416 \cdot 0.0021}

Next Step Evaluate

∴

ω s = 9.99999956595098Hz

Next Step Convert to Output's Unit

∴

ω s = 599.999973957059rev/min

LAST Step Rounding Answer

∴

ω s = 600rev/min

Rotational Frequency of Spindle given Cutting Speed Formula Elements

Variables

Constants

Rotational Frequency of Spindle

Rotational Frequency of Spindle is the speed at which the spindle of a machine tool rotates during machining operations. It is typically measured in revolutions per minute.

Symbol: ω_s

Measurement: FrequencyUnit: rev/min

Note: Value should be greater than 0.

Formulas to find Rotational Frequency of Spindle

Cutting Velocity

The Cutting Velocity is the tangential velocity at the periphery of the cutter or workpiece (whichever is rotating).

Symbol: V

Measurement: SpeedUnit: mm/min

Note: Value should be greater than 0.

Formulas to find Cutting Velocity

Instantaneous Radius for Cut

Instantaneous Radius for Cut is the effective radius of the cutting tool at a specific moment during the machining process.

Symbol: r

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Instantaneous Radius for Cut

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

Other Formulas to find Rotational Frequency of Spindle

Go Optimum Spindle Speed

ω s = (\frac{V s}{2 \cdot π \cdot R o}) \cdot {(\frac{(1 + n) \cdot C t \cdot T ref \cdot (1 - R w)}{(1 - n) \cdot (C t \cdot t c + C t) \cdot (1 - {R w}^{\frac{1 + n}{n}})})}^{n}

Go Optimum Spindle Speed given Tool Changing Cost

ω s = (\frac{V ref}{2 \cdot π \cdot R o}) \cdot {(\frac{(1 + n) \cdot C t \cdot T max \cdot (1 - R w)}{(1 - n) \cdot (C ct + C t) \cdot (1 - {R w}^{\frac{1 + n}{n}})})}^{n}

Other formulas in Cutting Speed category

Go Reference Cutting Velocity given Rate of Increase of Wear-Land Width

V ref = \frac{V}{{(V r \cdot \frac{T ref}{w})}^{n}}

Go Cutting Velocity given Rate of Increase of Wear-Land Width

V = V ref \cdot {(V r \cdot \frac{T ref}{w})}^{n}

Go Instantaneous Cutting Speed

V = 2 \cdot π \cdot ω s \cdot r

Go Time for Facing given Instantaneous Cutting Speed

t = \frac{R o - (\frac{V}{2 \cdot π \cdot ω s})}{ω s \cdot f}

How to Evaluate Rotational Frequency of Spindle given Cutting Speed?

Rotational Frequency of Spindle given Cutting Speed evaluator uses Rotational Frequency of Spindle = Cutting Velocity/(2*pi*Instantaneous Radius for Cut) to evaluate the Rotational Frequency of Spindle, The Rotational Frequency of Spindle given Cutting Speed is a method to determine the required frequency of rotation of the Spindle of a Machining Tool such that the Cutting Speed on the Workpiece remains constant at any given time. Rotational Frequency of Spindle is denoted by ω_s symbol.

How to evaluate Rotational Frequency of Spindle given Cutting Speed using this online evaluator? To use this online evaluator for Rotational Frequency of Spindle given Cutting Speed, enter Cutting Velocity (V) & Instantaneous Radius for Cut (r) and hit the calculate button.

FAQs on Rotational Frequency of Spindle given Cutting Speed

What is the formula to find Rotational Frequency of Spindle given Cutting Speed?

The formula of Rotational Frequency of Spindle given Cutting Speed is expressed as Rotational Frequency of Spindle = Cutting Velocity/(2*pi*Instantaneous Radius for Cut). Here is an example- 36000 = 0.133333333333333/(2*pi*0.002122066).

How to calculate Rotational Frequency of Spindle given Cutting Speed?

With Cutting Velocity (V) & Instantaneous Radius for Cut (r) we can find Rotational Frequency of Spindle given Cutting Speed using the formula - Rotational Frequency of Spindle = Cutting Velocity/(2*pi*Instantaneous Radius for Cut). This formula also uses Archimedes' constant .

What are the other ways to Calculate Rotational Frequency of Spindle?

Here are the different ways to Calculate Rotational Frequency of Spindle-

Rotational Frequency of Spindle=(Reference Cutting Velocity Spindle Speed/(2*pi*Outer Radius of Workpiece))*(((1+Taylor's Tool Life Exponent)*Cost of a Tool*Reference Tool Life*(1-Workpiece Radius Ratio))/((1-Taylor's Tool Life Exponent)*(Cost of a Tool*Time to Change One Tool+Cost of a Tool)*(1-Workpiece Radius Ratio^((1+Taylor's Tool Life Exponent)/Taylor's Tool Life Exponent))))^Taylor's Tool Life Exponent
Rotational Frequency of Spindle=(Reference Cutting Velocity/(2*pi*Outer Radius of Workpiece))*(((1+Taylor's Tool Life Exponent)*Cost of a Tool*Maximum Tool Life*(1-Workpiece Radius Ratio))/((1-Taylor's Tool Life Exponent)*(Cost of Changing Each Tool+Cost of a Tool)*(1-Workpiece Radius Ratio^((1+Taylor's Tool Life Exponent)/Taylor's Tool Life Exponent))))^Taylor's Tool Life Exponent

Can the Rotational Frequency of Spindle given Cutting Speed be negative?

No, the Rotational Frequency of Spindle given Cutting Speed, measured in Frequency cannot be negative.

Which unit is used to measure Rotational Frequency of Spindle given Cutting Speed?

Rotational Frequency of Spindle given Cutting Speed is usually measured using the Revolution per Minute[rev/min] for Frequency. Hertz[rev/min], Petahertz[rev/min], Terahertz[rev/min] are the few other units in which Rotational Frequency of Spindle given Cutting Speed can be measured.

Let Others Know

✖

Facebook

Twitter

Copied!

Rotational Frequency of Spindle given Cutting Speed Formula

​GoOptimum Spindle Speed Formula

​GoOptimum Spindle Speed given Tool Changing Cost Formula

Rotational Frequency of Spindle given Cutting Speed Example

Rotational Frequency of Spindle given Cutting Speed Solution

Rotational Frequency of Spindle given Cutting Speed Formula Elements

Other Formulas to find Rotational Frequency of Spindle

Other formulas in Cutting Speed category

How to Evaluate Rotational Frequency of Spindle given Cutting Speed?

FAQs on Rotational Frequency of Spindle given Cutting Speed

Variable Name

GoOptimum Spindle Speed Formula

GoOptimum Spindle Speed given Tool Changing Cost Formula