Instantaneous Cutting Speed Calculator

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

✖The Cutting Velocity is the tangential velocity at the periphery of the cutter or workpiece (whichever is rotating).ⓘ Instantaneous Cutting Speed [V]

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Formula

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Instantaneous Cutting Speed

Formula

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

Example

`"8000mm/min"=2*pi*"10Hz"*"2.122066mm"`

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Instantaneous Cutting Speed Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

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).
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.
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

Rotational Frequency of Spindle: 10 Hertz --> 10 Hertz No Conversion Required
Instantaneous Radius for Cut: 2.122066 Millimeter --> 0.002122066 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

V = 2*pi*n_s*r --> 2*pi*10*0.002122066

Evaluating ... ...

V = 0.133333339120654

STEP 3: Convert Result to Output's Unit

0.133333339120654 Meter per Second -->8000.00034723921 Millimeter per Minute (Check conversion here)

FINAL ANSWER

8000.00034723921 ≈ 8000 Millimeter per Minute <-- Cutting Velocity

(Calculation completed in 00.004 seconds)

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Credits

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)^(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

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*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

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 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

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)

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

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

Instantaneous Cutting Speed Formula

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

Cutting Speed in Facing Operation

In a Facing Operation, a constant spindle speed results in a variable cutting speed which varies linearly with the radius of the cut. The cutting speed is maximum at the periphery of the workpiece and minimum at the end of the operation.

How to Calculate Instantaneous Cutting Speed?

Instantaneous Cutting Speed calculator uses Cutting Velocity = 2*pi*Rotational Frequency of Spindle*Instantaneous Radius for Cut to calculate the Cutting Velocity, The Instantaneous Cutting Speed is defined as the relative speed at which the Machining Tool cuts the surface of the workpiece at a particular instant. Cutting Velocity is denoted by V symbol.

How to calculate Instantaneous Cutting Speed using this online calculator? To use this online calculator for Instantaneous Cutting Speed, enter Rotational Frequency of Spindle (n_s) & Instantaneous Radius for Cut (r) and hit the calculate button. Here is how the Instantaneous Cutting Speed calculation can be explained with given input values -> 2.7E+10 = 2*pi*10*0.002122066.

FAQ

What is Instantaneous Cutting Speed?

The Instantaneous Cutting Speed is defined as the relative speed at which the Machining Tool cuts the surface of the workpiece at a particular instant and is represented as V = 2*pi*n_s*r or Cutting Velocity = 2*pi*Rotational Frequency of Spindle*Instantaneous Radius for Cut. Rotational Frequency of Spindle is the number of turns made by the spindle of the Machine for cutting in one second & Instantaneous Radius for Cut is the radius of the workpiece surface currently being machined.

How to calculate Instantaneous Cutting Speed?

The Instantaneous Cutting Speed is defined as the relative speed at which the Machining Tool cuts the surface of the workpiece at a particular instant is calculated using Cutting Velocity = 2*pi*Rotational Frequency of Spindle*Instantaneous Radius for Cut. To calculate Instantaneous Cutting Speed, you need Rotational Frequency of Spindle (n_s) & Instantaneous Radius for Cut (r). With our tool, you need to enter the respective value for Rotational Frequency of Spindle & 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 Cutting Velocity?

In this formula, Cutting Velocity uses Rotational Frequency of Spindle & Instantaneous Radius for Cut. We can use 3 other way(s) to calculate the same, which is/are as follows -

Cutting Velocity = Reference Cutting Velocity*(Rate of Increase of Wear Land Width*Reference Tool Life/Maximum Wear Land Width)^Taylor's Tool Life Exponent
Cutting Velocity = 2*pi*Rotational Frequency of Spindle*(Outer Radius of Workpiece-Rotational Frequency of Spindle*Feed*Process Time)
Cutting Velocity = (Reference Tool Life/(Tool Life*Time Proportion of Cutting Edge Engagement))^Taylor's Tool Life Exponent*Reference Cutting Velocity

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