Feed given Instantaneous Cutting Speed Calculator

✖Outer Radius of Workpiece is the radius of the outermost surface of the workpiece, away from the machining tool.ⓘ Outer Radius of Workpiece [R_o]			+10% -10%
✖The Cutting Velocity is the tangential velocity at the periphery of the cutter or workpiece (whichever is rotating).ⓘ Cutting Velocity [V]			+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 [n_s]			+10% -10%
✖Process Time is the time for which any Process has been carried out irrespective of its completion.ⓘ Process Time [t']			+10% -10%

✖The Feed is the distance the cutting tool advances along the length of the work for every revolution of the spindle.ⓘ Feed given Instantaneous Cutting Speed [f]

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Formula

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Feed given Instantaneous Cutting Speed

Formula

`"f" = ("R"_{"o"}-("V"/(2*pi*"n"_{"s"})))/("n"_{"s"}*"t'")`

Example

`"0.157902mm"=("10000mm"-("8000mm/min"/(2*pi*"10Hz")))/("10Hz"*"105.5282min")`

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Feed given Instantaneous Cutting Speed Solution

STEP 0: Pre-Calculation Summary

Formula Used

Feed = (Outer Radius of Workpiece-(Cutting Velocity/(2*pi*Rotational Frequency of Spindle)))/(Rotational Frequency of Spindle*Process Time)
f = (R_o-(V/(2*pi*n_s)))/(n_s*t')
This formula uses 1 Constants, 5 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Feed - (Measured in Meter) - The Feed is the distance the cutting tool advances along the length of the work for every revolution of the spindle.
Outer Radius of Workpiece - (Measured in Meter) - Outer Radius of Workpiece is the radius of the outermost surface of the workpiece, away from the machining tool.
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.
Process Time - (Measured in Second) - Process Time is the time for which any Process has been carried out irrespective of its completion.

STEP 1: Convert Input(s) to Base Unit

Outer Radius of Workpiece: 10000 Millimeter --> 10 Meter (Check conversion here)
Cutting Velocity: 8000 Millimeter per Minute --> 0.133333333333333 Meter per Second (Check conversion here)
Rotational Frequency of Spindle: 10 Hertz --> 10 Hertz No Conversion Required
Process Time: 105.5282 Minute --> 6331.692 Second (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

f = (R_o-(V/(2*pi*n_s)))/(n_s*t') --> (10-(0.133333333333333/(2*pi*10)))/(10*6331.692)

Evaluating ... ...

f = 0.000157902152127616

STEP 3: Convert Result to Output's Unit

0.000157902152127616 Meter -->0.157902152127616 Millimeter (Check conversion here)

FINAL ANSWER

0.157902152127616 ≈ 0.157902 Millimeter <-- Feed

(Calculation completed in 00.004 seconds)

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Home » Engineering » Production Engineering » Metal Machining » Facing Operation » Machine Tools and Operations » Cutting Speed » Feed given Instantaneous Cutting Speed

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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)^(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

Feed given Instantaneous Cutting Speed Formula

Feed = (Outer Radius of Workpiece-(Cutting Velocity/(2*pi*Rotational Frequency of Spindle)))/(Rotational Frequency of Spindle*Process Time)
f = (R_o-(V/(2*pi*n_s)))/(n_s*t')

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 Feed given Instantaneous Cutting Speed?

Feed given Instantaneous Cutting Speed calculator uses Feed = (Outer Radius of Workpiece-(Cutting Velocity/(2*pi*Rotational Frequency of Spindle)))/(Rotational Frequency of Spindle*Process Time) to calculate the Feed, The Feed given Instantaneous Cutting Speed is a method to determine the feed to be given for a Machining Tool when working under a given Cutting Speed of the Tool. Feed is denoted by f symbol.

How to calculate Feed given Instantaneous Cutting Speed using this online calculator? To use this online calculator for Feed given Instantaneous Cutting Speed, enter Outer Radius of Workpiece (R_o), Cutting Velocity (V), Rotational Frequency of Spindle (n_s) & Process Time (t') and hit the calculate button. Here is how the Feed given Instantaneous Cutting Speed calculation can be explained with given input values -> 78.93432 = (10-(0.133333333333333/(2*pi*10)))/(10*6331.692).

FAQ

What is Feed given Instantaneous Cutting Speed?

The Feed given Instantaneous Cutting Speed is a method to determine the feed to be given for a Machining Tool when working under a given Cutting Speed of the Tool and is represented as f = (R_o-(V/(2*pi*n_s)))/(n_s*t') or Feed = (Outer Radius of Workpiece-(Cutting Velocity/(2*pi*Rotational Frequency of Spindle)))/(Rotational Frequency of Spindle*Process Time). Outer Radius of Workpiece is the radius of the outermost surface of the workpiece, away from the machining tool, The Cutting Velocity is the tangential velocity at the periphery of the cutter or workpiece (whichever is rotating), Rotational Frequency of Spindle is the number of turns made by the spindle of the Machine for cutting in one second & Process Time is the time for which any Process has been carried out irrespective of its completion.

How to calculate Feed given Instantaneous Cutting Speed?

The Feed given Instantaneous Cutting Speed is a method to determine the feed to be given for a Machining Tool when working under a given Cutting Speed of the Tool is calculated using Feed = (Outer Radius of Workpiece-(Cutting Velocity/(2*pi*Rotational Frequency of Spindle)))/(Rotational Frequency of Spindle*Process Time). To calculate Feed given Instantaneous Cutting Speed, you need Outer Radius of Workpiece (R_o), Cutting Velocity (V), Rotational Frequency of Spindle (n_s) & Process Time (t'). With our tool, you need to enter the respective value for Outer Radius of Workpiece, Cutting Velocity, Rotational Frequency of Spindle & Process Time and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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