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Instantaneous Cutting Speed Formula

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

GoInstantaneous Cutting Speed given Feed 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

V - Cutting Velocity?ω_s - Rotational Frequency of Spindle?r - Instantaneous Radius for Cut?π - Archimedes' constant?

Instantaneous Cutting Speed Example

With values

With units

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

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

Here is how the Instantaneous Cutting Speed equation looks like.

8000.0003 = 2 \cdot 3.1416 \cdot 600 \cdot 2.1221

8000.0003mm/min = 2 \cdot 3.1416 \cdot 600rev/min \cdot 2.1221mm

8000.0003 = 2 \cdot 3.1416 \cdot 600 \cdot 2.1221

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Instantaneous Cutting Speed Solution

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

FIRST Step Consider the formula

V = 2 \cdot π \cdot ω s \cdot r

Next Step Substitute values of Variables

∴

V = 2 \cdot π \cdot 600rev/min \cdot 2.1221mm

Next Step Substitute values of Constants

∴

V = 2 \cdot 3.1416 \cdot 600rev/min \cdot 2.1221mm

Next Step Convert Units

∴

V = 2 \cdot 3.1416 \cdot 10Hz \cdot 0.0021m

Next Step Prepare to Evaluate

∴

V = 2 \cdot 3.1416 \cdot 10 \cdot 0.0021

Next Step Evaluate

∴

V = 0.133333339120654m/s

Next Step Convert to Output's Unit

∴

V = 8000.00034723921mm/min

LAST Step Rounding Answer

∴

V = 8000.0003mm/min

Instantaneous Cutting Speed 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

Instantaneous Radius for Cut

Instantaneous Radius for Cut is the effective radius of the cutting tool at a specific moment during the machining process.

Symbol: r

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Instantaneous Radius for Cut

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 given Feed

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

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?

Instantaneous Cutting Speed evaluator uses Cutting Velocity = 2*pi*Rotational Frequency of Spindle*Instantaneous Radius for Cut to evaluate the Cutting Velocity, The Instantaneous Cutting Speed refers to the linear velocity of a specific point on the cutting tool's cutting edge as it engages with the workpiece material during the machining process. It represents the speed at which the cutting edge moves relative to the workpiece surface at any given moment during machining. Cutting Velocity is denoted by V symbol.

How to evaluate Instantaneous Cutting Speed using this online evaluator? To use this online evaluator for Instantaneous Cutting Speed, enter Rotational Frequency of Spindle (ω_s) & Instantaneous Radius for Cut (r) and hit the calculate button.

FAQs on Instantaneous Cutting Speed

What is the formula to find Instantaneous Cutting Speed?

The formula of Instantaneous Cutting Speed is expressed as Cutting Velocity = 2*pi*Rotational Frequency of Spindle*Instantaneous Radius for Cut. Here is an example- 8E+6 = 2*pi*10*0.002122066.

How to calculate Instantaneous Cutting Speed?

With Rotational Frequency of Spindle (ω_s) & Instantaneous Radius for Cut (r) we can find Instantaneous Cutting Speed using the formula - Cutting Velocity = 2*pi*Rotational Frequency of Spindle*Instantaneous Radius for Cut. 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*(Outer Radius of Workpiece-Rotational Frequency of Spindle*Feed*Process Time)
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 be negative?

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

Which unit is used to measure Instantaneous Cutting Speed?

Instantaneous Cutting Speed 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 can be measured.

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Instantaneous Cutting Speed Formula

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

​GoInstantaneous Cutting Speed given Feed Formula

Instantaneous Cutting Speed Example

Instantaneous Cutting Speed Solution

Instantaneous Cutting Speed Formula Elements

Other Formulas to find Cutting Velocity

Other formulas in Cutting Speed category

How to Evaluate Instantaneous Cutting Speed?

FAQs on Instantaneous Cutting Speed

Variable Name

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

GoInstantaneous Cutting Speed given Feed Formula