Rotational Frequency of Spindle given Cutting Speed Calculator

✖The Cutting Velocity is the tangential velocity at the periphery of the cutter or workpiece (whichever is rotating).ⓘ Cutting Velocity [V]			+10% -10%
✖Instantaneous Radius for Cut is the effective radius of the cutting tool at a specific moment during the machining process.ⓘ Instantaneous Radius for Cut [r]			+10% -10%

✖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.ⓘ Rotational Frequency of Spindle given Cutting Speed [n_s]

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Rotational Frequency of Spindle given Cutting Speed

Formula

`"n"_{"s"} = "V"/(2*pi*"r")`

Example

`"600rev/min"="8000mm/min"/(2*pi*"2.122066mm")`

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Rotational Frequency of Spindle given Cutting Speed Solution

STEP 0: Pre-Calculation Summary

Formula Used

Rotational Frequency of Spindle = Cutting Velocity/(2*pi*Instantaneous Radius for Cut)
n_s = V/(2*pi*r)
This formula uses 1 Constants, 3 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Rotational Frequency of Spindle - (Measured in Hertz) - 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.
Cutting Velocity - (Measured in Meter per Second) - The Cutting Velocity is the tangential velocity at the periphery of the cutter or workpiece (whichever is rotating).
Instantaneous Radius for Cut - (Measured in Meter) - Instantaneous Radius for Cut is the effective radius of the cutting tool at a specific moment during the machining process.

STEP 1: Convert Input(s) to Base Unit

Cutting Velocity: 8000 Millimeter per Minute --> 0.133333333333333 Meter per Second (Check conversion here)
Instantaneous Radius for Cut: 2.122066 Millimeter --> 0.002122066 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

n_s = V/(2*pi*r) --> 0.133333333333333/(2*pi*0.002122066)

Evaluating ... ...

n_s = 9.99999956595098

STEP 3: Convert Result to Output's Unit

9.99999956595098 Hertz -->599.999973957059 Revolution per Minute (Check conversion here)

FINAL ANSWER

599.999973957059 ≈ 600 Revolution per Minute <-- Rotational Frequency of Spindle

(Calculation completed in 00.004 seconds)

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Created by Kumar Siddhant

Indian Institute of Information Technology, Design and Manufacturing (IIITDM), Jabalpur

Kumar Siddhant has created this Calculator and 400+ more calculators!

Verified by Parul Keshav

National Institute of Technology (NIT), Srinagar

Parul Keshav has verified this Calculator and 400+ more calculators!

< 21 Cutting Speed Calculators

Reference Tool Life given Optimum Spindle Speed

Go Reference Tool Life = ((Rotational Frequency of Spindle*2*pi*Outer Radius of Workpiece/Reference Cutting Velocity Spindle Speed)^(1/Taylor's Tool Life Exponent)*(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)))/((1+Taylor's Tool Life Exponent)*Cost of a Tool*(1-Workpiece Radius Ratio))

Optimum Spindle Speed

Go 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

Reference Cutting Velocity given Optimum Spindle Speed

Go Reference Cutting Velocity Spindle Speed = Rotational Frequency of Spindle*2*pi*Outer Radius of Workpiece*(((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)))/((1+Taylor's Tool Life Exponent)*Cost of a Tool*Reference Tool Life*(1-Workpiece Radius Ratio)))^Taylor's Tool Life Exponent

Machining and Operating Rate given Optimum Spindle Speed

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

Tool Changing Time given Optimum Spindle Speed

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

Cost of 1 Tool given Optimum Spindle Speed

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

Tool Changing Cost given Optimum Spindle Speed

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

Optimum Spindle Speed given Tool Changing Cost

Go 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

Taylor's Exponent given Cutting Speed for Constant-Cutting-Speed Operation

Go Taylor's Tool Life Exponent = ln(Cutting Velocity/Reference Cutting Velocity)/ln(Reference Tool Life/(Tool Life*Time Proportion of Cutting Edge))

Time for Facing given Instantaneous Cutting Speed

Go Process Time = (Outer Radius of Workpiece-(Cutting Velocity/(2*pi*Rotational Frequency of Spindle)))/(Rotational Frequency of Spindle*Feed)

Feed given Instantaneous Cutting Speed

Go Feed = (Outer Radius of Workpiece-(Cutting Velocity/(2*pi*Rotational Frequency of Spindle)))/(Rotational Frequency of Spindle*Process Time)

Instantaneous Cutting Speed given Feed

Go Cutting Velocity = 2*pi*Rotational Frequency of Spindle*(Outer Radius of Workpiece-Rotational Frequency of Spindle*Feed*Process Time)

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

Go Reference Cutting Velocity = Cutting Velocity/((Rate of Increase of Wear Land Width*Reference Tool Life/Maximum Wear Land Width)^Taylor's Tool Life Exponent)

Cutting Velocity given Rate of Increase of Wear-Land Width

Go Cutting Velocity = Reference Cutting Velocity*(Rate of Increase of Wear Land Width*Reference Tool Life/Maximum Wear Land Width)^Taylor's Tool Life Exponent

Time Proportion of Edge given Cutting Speed for Constant-Cutting-Speed Operation

Go Time Proportion of Cutting Edge = Reference Tool Life*((Reference Cutting Velocity/Cutting Velocity)^(1/Taylor's Tool Life Exponent))/Tool Life

Tool Life given Cutting Speed for Constant-Cutting-Speed Operation

Go Tool Life = Reference Tool Life*((Reference Cutting Velocity/Cutting Velocity)^(1/Taylor's Tool Life Exponent))/Time Proportion of Cutting Edge

Reference Cutting Velocity given Cutting Velocity for Constant-Cutting-Speed Operation

Go Reference Cutting Velocity = Cutting Velocity/((Reference Tool Life/(Tool Life*Time Proportion of Cutting Edge))^Taylor's Tool Life Exponent)

Reference Tool Life given Cutting Speed for Constant-Cutting-Speed Operation

Go Reference Tool Life = (Cutting Velocity/Reference Cutting Velocity)^(1/Taylor's Tool Life Exponent)*Time Proportion of Cutting Edge*Tool Life

Cutting Speed for Constant-Cutting-Speed Operation

Go Cutting Velocity = (Reference Tool Life/(Tool Life*Time Proportion of Cutting Edge))^Taylor's Tool Life Exponent*Reference Cutting Velocity

Rotational Frequency of Spindle given Cutting Speed

Go Rotational Frequency of Spindle = Cutting Velocity/(2*pi*Instantaneous Radius for Cut)

Instantaneous Cutting Speed

Go Cutting Velocity = 2*pi*Rotational Frequency of Spindle*Instantaneous Radius for Cut

Rotational Frequency of Spindle given Cutting Speed Formula

Rotational Frequency of Spindle = Cutting Velocity/(2*pi*Instantaneous Radius for Cut)
n_s = V/(2*pi*r)

Main Spindle Errors

Accuracy of spindle error measurement is affected by inherent error sources such as:
1. Sensor offset
2. Thermal drift of spindle
3. Centering error
4. Form error of the target surface installed in the spindle.

How to Calculate Rotational Frequency of Spindle given Cutting Speed?

Rotational Frequency of Spindle given Cutting Speed calculator uses Rotational Frequency of Spindle = Cutting Velocity/(2*pi*Instantaneous Radius for Cut) to calculate 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 n_s symbol.

How to calculate Rotational Frequency of Spindle given Cutting Speed using this online calculator? To use this online calculator for Rotational Frequency of Spindle given Cutting Speed, enter Cutting Velocity (V) & Instantaneous Radius for Cut (r) and hit the calculate button. Here is how the Rotational Frequency of Spindle given Cutting Speed calculation can be explained with given input values -> 36000 = 0.133333333333333/(2*pi*0.002122066).

FAQ

What is Rotational Frequency of Spindle given Cutting Speed?

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 and is represented as n_s = V/(2*pi*r) or Rotational Frequency of Spindle = Cutting Velocity/(2*pi*Instantaneous Radius for Cut). The Cutting Velocity is the tangential velocity at the periphery of the cutter or workpiece (whichever is rotating) & Instantaneous Radius for Cut is the effective radius of the cutting tool at a specific moment during the machining process.

How to calculate Rotational Frequency of Spindle given Cutting Speed?

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 is calculated using Rotational Frequency of Spindle = Cutting Velocity/(2*pi*Instantaneous Radius for Cut). To calculate Rotational Frequency of Spindle given Cutting Speed, you need Cutting Velocity (V) & Instantaneous Radius for Cut (r). With our tool, you need to enter the respective value for Cutting Velocity & Instantaneous Radius for Cut and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Rotational Frequency of Spindle?

In this formula, Rotational Frequency of Spindle uses Cutting Velocity & Instantaneous Radius for Cut. We can use 2 other way(s) to calculate the same, which is/are as follows -

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

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