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Outside Radius of Workpiece given Instantaneous Cutting Speed Formula

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GoOutside Radius of Workpiece given Instantaneous Radius for Cut Formula

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GoOutside Radius given Workpiece Radius Ratio Formula

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Outside Radius of the Workpiece is the radius of the outermost surface of the workpiece, away from the machining tool. Check FAQs

r o = (\frac{V}{2 \cdot π \cdot ω s}) + ω s \cdot f \cdot t′

r_o - Outside Radius of The Workpiece?V - Cutting Velocity?ω_s - Rotational Frequency of Spindle?f - Feed?t′ - Process Time?π - Archimedes' constant?

Outside Radius of Workpiece given Instantaneous Cutting Speed Example

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Here is how the Outside Radius of Workpiece given Instantaneous Cutting Speed equation looks like with Values.

Here is how the Outside Radius of Workpiece given Instantaneous Cutting Speed equation looks like with Units.

Here is how the Outside Radius of Workpiece given Instantaneous Cutting Speed equation looks like.

8063.9977 = (\frac{452.3892}{2 \cdot 3.1416 \cdot 10}) + 10 \cdot 0.9 \cdot 1.6

8063.9977mm = (\frac{452.3892m/s}{2 \cdot 3.1416 \cdot 10Hz}) + 10Hz \cdot 0.9mm \cdot 1.6min

8063.9977 = (\frac{452.3892}{2 \cdot 3.1416 \cdot 10}) + 10 \cdot 0.9 \cdot 1.6

Tip: Use pencil () icon above to edit Input Values and Units.

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Outside Radius of Workpiece given Instantaneous Cutting Speed Solution

Follow our step by step solution on how to calculate Outside Radius of Workpiece given Instantaneous Cutting Speed?

FIRST Step Consider the formula

r o = (\frac{V}{2 \cdot π \cdot ω s}) + ω s \cdot f \cdot t′

Next Step Substitute values of Variables

∴

r o = (\frac{452.3892m/s}{2 \cdot π \cdot 10Hz}) + 10Hz \cdot 0.9mm \cdot 1.6min

Next Step Substitute values of Constants

∴

r o = (\frac{452.3892m/s}{2 \cdot 3.1416 \cdot 10Hz}) + 10Hz \cdot 0.9mm \cdot 1.6min

Next Step Convert Units

∴

r o = (\frac{452.3892m/s}{2 \cdot 3.1416 \cdot 10Hz}) + 10Hz \cdot 0.0009m \cdot 96s

Next Step Prepare to Evaluate

∴

r o = (\frac{452.3892}{2 \cdot 3.1416 \cdot 10}) + 10 \cdot 0.0009 \cdot 96

Next Step Evaluate

∴

r o = 8.06399773813881m

Next Step Convert to Output's Unit

∴

r o = 8063.99773813881mm

LAST Step Rounding Answer

∴

r o = 8063.9977mm

Outside Radius of Workpiece given Instantaneous Cutting Speed Formula Elements

Variables

Constants

Outside Radius of The Workpiece

Outside Radius of the Workpiece is the radius of the outermost surface of the workpiece, away from the machining tool.

Symbol: r_o

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Cutting Velocity

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

Symbol: V

Measurement: SpeedUnit: m/s

Note: Value should be greater than 0.

Rotational Frequency of Spindle

Rotational Frequency of Spindle is the number of turns made by the spindle of the Machine for cutting in one second.

Symbol: ω_s

Measurement: FrequencyUnit: Hz

Note: Value should be greater than 0.

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.

Process Time

Process Time is the time for which any process has been carried out irrespective of its completion.

Symbol: t′

Measurement: TimeUnit: min

Note: Value should be greater than 0.

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

Credits

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Created by Kumar Siddhant

Indian Institute of Information Technology, Design and Manufacturing (IIITDM), Jabalpur

Kumar Siddhant has created this Formula and 400+ more formulas!

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Verified by Parul Keshav

National Institute of Technology (NIT), Srinagar

Parul Keshav has verified this Formula and 400+ more formulas!

Other Formulas to find Outside Radius of The Workpiece

Go Outside Radius of Workpiece given Instantaneous Radius for Cut

r o = r + ω s \cdot f \cdot t′

Go Outside Radius given Workpiece Radius Ratio

r o = \frac{r i}{R w}

Go Outside Radius of Workpiece given Optimum Spindle Speed

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

Other formulas in Instantaneous Radius category

Go Instantaneous Radius for Cut given Cutting Speed

r = \frac{V}{2 \cdot π \cdot ω s}

Go Instantaneous Radius for Cut given Rate of Increase of Wear-Land

r = \frac{V ref \cdot {(W r \cdot \frac{L ref}{W max})}^{n}}{2 \cdot π \cdot ω s}

Go Instantaneous Radius for Cut

r = r o - ω s \cdot f \cdot t′

Go Feed given Instantaneous Radius for Cut

f = \frac{r o - r}{ω s \cdot t′}

See More

How to Evaluate Outside Radius of Workpiece given Instantaneous Cutting Speed?

Outside Radius of Workpiece given Instantaneous Cutting Speed evaluator uses Outside Radius of The Workpiece = (Cutting Velocity/(2*pi*Rotational Frequency of Spindle))+Rotational Frequency of Spindle*Feed*Process Time to evaluate the Outside Radius of The Workpiece, The Outside Radius of Workpiece given Instantaneous Cutting Speed is a method to determine the radius of the outermost surface of the workpiece, away from the machining tool, when the working Cutting Speed of Tool is known. Outside Radius of The Workpiece is denoted by r_o symbol.

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

FAQs on Outside Radius of Workpiece given Instantaneous Cutting Speed

What is the formula to find Outside Radius of Workpiece given Instantaneous Cutting Speed?

The formula of Outside Radius of Workpiece given Instantaneous Cutting Speed is expressed as Outside Radius of The Workpiece = (Cutting Velocity/(2*pi*Rotational Frequency of Spindle))+Rotational Frequency of Spindle*Feed*Process Time. Here is an example- 984000 = (452.3892/(2*pi*10))+10*0.0009*96.

How to calculate Outside Radius of Workpiece given Instantaneous Cutting Speed?

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

What are the other ways to Calculate Outside Radius of The Workpiece?

Here are the different ways to Calculate Outside Radius of The Workpiece-

Outside Radius of The Workpiece=Instantaneous Radius For Cut+Rotational Frequency of Spindle*Feed*Process Time
Outside Radius of The Workpiece=Inner Radius of Workpiece/Workpiece Radius Ratio
Outside Radius of The Workpiece=(Reference Cutting Velocity/(2*pi*Rotational Frequency of Spindle))*(((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

Can the Outside Radius of Workpiece given Instantaneous Cutting Speed be negative?

No, the Outside Radius of Workpiece given Instantaneous Cutting Speed, measured in Length cannot be negative.

Which unit is used to measure Outside Radius of Workpiece given Instantaneous Cutting Speed?

Outside Radius of Workpiece given Instantaneous Cutting Speed is usually measured using the Millimeter[mm] for Length. Meter[mm], Kilometer[mm], Decimeter[mm] are the few other units in which Outside Radius of Workpiece given Instantaneous Cutting Speed can be measured.

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