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Instantaneous Cutting Speed given Feed Formula

GoCutting Velocity given Rate of Increase of Wear-Land Width Formula

GoInstantaneous Cutting Speed Formula

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The Cutting Velocity is the tangential velocity at the periphery of the cutter or workpiece (whichever is rotating). Check FAQs

V = 2 \cdot π \cdot ω s \cdot (R o - ω s \cdot f \cdot t)

V - Cutting Velocity?ω_s - Rotational Frequency of Spindle?R_o - Outer Radius of Workpiece?f - Feed?t - Process Time?π - Archimedes' constant?

Instantaneous Cutting Speed given Feed Example

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With units

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Here is how the Instantaneous Cutting Speed given Feed equation looks like with Values.

Here is how the Instantaneous Cutting Speed given Feed equation looks like with Units.

Here is how the Instantaneous Cutting Speed given Feed equation looks like.

8000.0003 = 2 \cdot 3.1416 \cdot 600 \cdot (1000 - 600 \cdot 0.3008 \cdot 5.5282)

8000.0003mm/min = 2 \cdot 3.1416 \cdot 600rev/min \cdot (1000mm - 600rev/min \cdot 0.3008mm \cdot 5.5282min)

8000.0003 = 2 \cdot 3.1416 \cdot 600 \cdot (1000 - 600 \cdot 0.3008 \cdot 5.5282)

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Instantaneous Cutting Speed given Feed Solution

Follow our step by step solution on how to calculate Instantaneous Cutting Speed given Feed?

FIRST Step Consider the formula

V = 2 \cdot π \cdot ω s \cdot (R o - ω s \cdot f \cdot t)

Next Step Substitute values of Variables

∴

V = 2 \cdot π \cdot 600rev/min \cdot (1000mm - 600rev/min \cdot 0.3008mm \cdot 5.5282min)

Next Step Substitute values of Constants

∴

V = 2 \cdot 3.1416 \cdot 600rev/min \cdot (1000mm - 600rev/min \cdot 0.3008mm \cdot 5.5282min)

Next Step Convert Units

∴

V = 2 \cdot 3.1416 \cdot 10Hz \cdot (1m - 10Hz \cdot 0.0003m \cdot 331.692s)

Next Step Prepare to Evaluate

∴

V = 2 \cdot 3.1416 \cdot 10 \cdot (1 - 10 \cdot 0.0003 \cdot 331.692)

Next Step Evaluate

∴

V = 0.133333338760997m/s

Next Step Convert to Output's Unit

∴

V = 8000.00032565983mm/min

LAST Step Rounding Answer

∴

V = 8000.0003mm/min

Instantaneous Cutting Speed given Feed Formula Elements

Variables

Constants

Cutting Velocity

The Cutting Velocity is the tangential velocity at the periphery of the cutter or workpiece (whichever is rotating).

Symbol: V

Measurement: SpeedUnit: mm/min

Note: Value should be greater than 0.

Formulas to find Cutting Velocity

Rotational Frequency of Spindle

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.

Symbol: ω_s

Measurement: FrequencyUnit: rev/min

Note: Value should be greater than 0.

Formulas to find Rotational Frequency of Spindle

Outer Radius of Workpiece

Outer Radius of Workpiece is the distance from the center of rotation to the outermost surface of the workpiece being machined.

Symbol: R_o

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Outer Radius of Workpiece

Feed

The Feed is the distance the cutting tool advances along the length of the work for every revolution of the spindle.

Symbol: f

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Feed

Process Time

Process Time refers to the duration it takes to complete a specific operation or set of operations involved in the manufacturing process.

Symbol: t

Measurement: TimeUnit: min

Note: Value should be greater than 0.

Formulas to find Process Time

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

Other Formulas to find Cutting Velocity

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

V = V ref \cdot {(V r \cdot \frac{T ref}{w})}^{n}

Go Instantaneous Cutting Speed

V = 2 \cdot π \cdot ω s \cdot r

Go Cutting Speed for Constant-Cutting-Speed Operation

V = {(\frac{T ref}{L \cdot Q})}^{n} \cdot V ref

Other formulas in Cutting Speed category

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

V ref = \frac{V}{{(V r \cdot \frac{T ref}{w})}^{n}}

Go Time for Facing given Instantaneous Cutting Speed

t = \frac{R o - (\frac{V}{2 \cdot π \cdot ω s})}{ω s \cdot f}

Go Feed given Instantaneous Cutting Speed

f = \frac{R o - (\frac{V}{2 \cdot π \cdot ω s})}{ω s \cdot t}

Go Optimum Spindle Speed

ω s = (\frac{V s}{2 \cdot π \cdot R o}) \cdot {(\frac{(1 + n) \cdot C t \cdot T ref \cdot (1 - R w)}{(1 - n) \cdot (C t \cdot t c + C t) \cdot (1 - {R w}^{\frac{1 + n}{n}})})}^{n}

How to Evaluate Instantaneous Cutting Speed given Feed?

Instantaneous Cutting Speed given Feed evaluator uses Cutting Velocity = 2*pi*Rotational Frequency of Spindle*(Outer Radius of Workpiece-Rotational Frequency of Spindle*Feed*Process Time) to evaluate the Cutting Velocity, The Instantaneous Cutting Speed given Feed is a critical parameter in metal machining as it directly influences various aspects of the machining process, including material removal rates, tool wear rates, cutting forces, and surface finish quality. Machinists adjust cutting speeds based on factors such as the material being machined, tool material and geometry, cutting parameters, and desired machining outcomes to achieve optimal performance and efficiency. Cutting Velocity is denoted by V symbol.

How to evaluate Instantaneous Cutting Speed given Feed using this online evaluator? To use this online evaluator for Instantaneous Cutting Speed given Feed, enter Rotational Frequency of Spindle (ω_s), Outer Radius of Workpiece (R_o), Feed (f) & Process Time (t) and hit the calculate button.

FAQs on Instantaneous Cutting Speed given Feed

What is the formula to find Instantaneous Cutting Speed given Feed?

The formula of Instantaneous Cutting Speed given Feed is expressed as Cutting Velocity = 2*pi*Rotational Frequency of Spindle*(Outer Radius of Workpiece-Rotational Frequency of Spindle*Feed*Process Time). Here is an example- 3.7E+9 = 2*pi*10*(1-10*0.0003008447397*331.692).

How to calculate Instantaneous Cutting Speed given Feed?

With Rotational Frequency of Spindle (ω_s), Outer Radius of Workpiece (R_o), Feed (f) & Process Time (t) we can find Instantaneous Cutting Speed given Feed using the formula - Cutting Velocity = 2*pi*Rotational Frequency of Spindle*(Outer Radius of Workpiece-Rotational Frequency of Spindle*Feed*Process Time). This formula also uses Archimedes' constant .

What are the other ways to Calculate Cutting Velocity?

Here are the different ways to Calculate Cutting Velocity-

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*Instantaneous Radius for Cut
Cutting Velocity=(Reference Tool Life/(Tool Life*Time Proportion of Cutting Edge))^Taylor's Tool Life Exponent*Reference Cutting Velocity

Can the Instantaneous Cutting Speed given Feed be negative?

No, the Instantaneous Cutting Speed given Feed, measured in Speed cannot be negative.

Which unit is used to measure Instantaneous Cutting Speed given Feed?

Instantaneous Cutting Speed given Feed is usually measured using the Millimeter per Minute[mm/min] for Speed. Meter per Second[mm/min], Meter per Minute[mm/min], Meter per Hour[mm/min] are the few other units in which Instantaneous Cutting Speed given Feed can be measured.

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Instantaneous Cutting Speed given Feed Formula

​GoCutting Velocity given Rate of Increase of Wear-Land Width Formula

​GoInstantaneous Cutting Speed Formula

Instantaneous Cutting Speed given Feed Example

Instantaneous Cutting Speed given Feed Solution

Instantaneous Cutting Speed given Feed Formula Elements

Other Formulas to find Cutting Velocity

Other formulas in Cutting Speed category

How to Evaluate Instantaneous Cutting Speed given Feed?

FAQs on Instantaneous Cutting Speed given Feed

Variable Name

GoCutting Velocity given Rate of Increase of Wear-Land Width Formula

GoInstantaneous Cutting Speed Formula