✖Outer Radius of Workpiece is the distance from the center of rotation to the outermost surface of the workpiece being machined.ⓘ 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 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 [ω_s]			+10% -10%
✖Process Time refers to the duration it takes to complete a specific operation or set of operations involved in the manufacturing process.ⓘ 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*"ω"_{"s"})))/("ω"_{"s"}*"t")`

Example

`"0.300845mm"=("1000mm"-("8000mm/min"/(2*pi*"600rev/min")))/("600rev/min"*"5.5282min")`

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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*ω_s)))/(ω_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 distance from the center of rotation to the outermost surface of the workpiece being machined.
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 speed at which the spindle of a machine tool rotates during machining operations. It is typically measured in revolutions per minute.
Process Time - (Measured in Second) - Process Time refers to the duration it takes to complete a specific operation or set of operations involved in the manufacturing process.

STEP 1: Convert Input(s) to Base Unit

Outer Radius of Workpiece: 1000 Millimeter --> 1 Meter (Check conversion here)
Cutting Velocity: 8000 Millimeter per Minute --> 0.133333333333333 Meter per Second (Check conversion here)
Rotational Frequency of Spindle: 600 Revolution per Minute --> 10 Hertz (Check conversion here)
Process Time: 5.5282 Minute --> 331.692 Second (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

f = (R_o-(V/(2*pi*ω_s)))/(ω_s*t) --> (1-(0.133333333333333/(2*pi*10)))/(10*331.692)

Evaluating ... ...

f = 0.000300844739726043

STEP 3: Convert Result to Output's Unit

0.000300844739726043 Meter -->0.300844739726043 Millimeter (Check conversion here)

FINAL ANSWER

0.300844739726043 ≈ 0.300845 Millimeter <-- Feed

(Calculation completed in 00.008 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

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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 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

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*ω_s)))/(ω_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. The feed refers to the linear distance the cutting tool travels along the workpiece surface per revolution or per unit of time. It's a crucial parameter that, along with the cutting speed (or velocity) and depth of cut, determines the material removal rate and the quality of the machined surface. 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 (ω_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 -> 15785.9 = (1-(0.133333333333333/(2*pi*10)))/(10*331.692).

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. The feed refers to the linear distance the cutting tool travels along the workpiece surface per revolution or per unit of time. It's a crucial parameter that, along with the cutting speed (or velocity) and depth of cut, determines the material removal rate and the quality of the machined surface and is represented as f = (R_o-(V/(2*pi*ω_s)))/(ω_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 distance from the center of rotation to the outermost surface of the workpiece being machined, The Cutting Velocity is the tangential velocity at the periphery of the cutter or workpiece (whichever is rotating), 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 & Process Time refers to the duration it takes to complete a specific operation or set of operations involved in the manufacturing process.

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. The feed refers to the linear distance the cutting tool travels along the workpiece surface per revolution or per unit of time. It's a crucial parameter that, along with the cutting speed (or velocity) and depth of cut, determines the material removal rate and the quality of the machined surface 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 (ω_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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