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 radius of the workpiece surface currently being machined.ⓘ Instantaneous Radius for Cut [r]			+10% -10%

✖Rotational Frequency of Spindle is the number of turns made by the spindle of the Machine for cutting in one second.ⓘ 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

`"0.176839Hz"="8000mm/min"/(2*pi*"120mm")`

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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 number of turns made by the spindle of the Machine for cutting in one second.
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 radius of the workpiece surface currently being machined.

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: 120 Millimeter --> 0.12 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

n_s = V/(2*pi*r) --> 0.133333333333333/(2*pi*0.12)

Evaluating ... ...

n_s = 0.176838825657661

STEP 3: Convert Result to Output's Unit

0.176838825657661 Hertz --> No Conversion Required

FINAL ANSWER

0.176838825657661 ≈ 0.176839 Hertz <-- 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

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Verified by Parul Keshav

National Institute of Technology (NIT), Srinagar

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< 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)^(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/(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 = Rotational Frequency of Spindle*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)

Machining and Operating Rate given Optimum Spindle Speed

Go Machining and Operating Rate = (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)

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 Time given Optimum Spindle Speed

Go Time to Change One Tool = Reference 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/Machining and Operating Rate

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*Reference 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)

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

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

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

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 Engagement given Cutting Speed for Constant-Cutting-Speed Operation

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

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 Engagement*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 Engagement

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

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

Cutting Speed for Constant-Cutting-Speed Operation

Go Cutting Velocity = (Reference Tool Life/(Tool Life*Time Proportion of Cutting Edge Engagement))^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 -> 0.176839 = 0.133333333333333/(2*pi*0.12).

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 radius of the workpiece surface currently being machined.

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/(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*Reference 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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