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

GoInstantaneous Radius for Cut given Cutting Speed Formula

GoInstantaneous Radius for Cut Formula

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Instantaneous Radius for Cut is the radius of the workpiece surface currently being machined. Check FAQs

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

r - Instantaneous Radius For Cut?V_ref - Reference Cutting Velocity?W_r - Rate of Increase of Wear Land Width?L_ref - Reference Tool Life?W_max - Maximum Wear Land Width?n - Taylor's Tool Life Exponent?ω_s - Rotational Frequency of Spindle?π - Archimedes' constant?

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

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Here is how the Instantaneous Radius for Cut given Rate of Increase of Wear-Land equation looks like with Values.

Here is how the Instantaneous Radius for Cut given Rate of Increase of Wear-Land equation looks like with Units.

Here is how the Instantaneous Radius for Cut given Rate of Increase of Wear-Land equation looks like.

53211.2906 = \frac{1050 \cdot {(0.543 \cdot \frac{5}{16066.91})}^{0.5}}{2 \cdot 3.1416 \cdot 10}

53211.2906mm = \frac{1050m/s \cdot {(0.543m/s \cdot \frac{5min}{16066.91mm})}^{0.5}}{2 \cdot 3.1416 \cdot 10Hz}

53211.2906 = \frac{1050 \cdot {(0.543 \cdot \frac{5}{16066.91})}^{0.5}}{2 \cdot 3.1416 \cdot 10}

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

Follow our step by step solution on how to calculate Instantaneous Radius for Cut given Rate of Increase of Wear-Land?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

r = \frac{1050m/s \cdot {(0.543m/s \cdot \frac{5min}{16066.91mm})}^{0.5}}{2 \cdot π \cdot 10Hz}

Next Step Substitute values of Constants

∴

r = \frac{1050m/s \cdot {(0.543m/s \cdot \frac{5min}{16066.91mm})}^{0.5}}{2 \cdot 3.1416 \cdot 10Hz}

Next Step Convert Units

∴

r = \frac{1050m/s \cdot {(0.543m/s \cdot \frac{300s}{16.0669m})}^{0.5}}{2 \cdot 3.1416 \cdot 10Hz}

Next Step Prepare to Evaluate

∴

r = \frac{1050 \cdot {(0.543 \cdot \frac{300}{16.0669})}^{0.5}}{2 \cdot 3.1416 \cdot 10}

Next Step Evaluate

∴

r = 53.2112905812559m

Next Step Convert to Output's Unit

∴

r = 53211.2905812559mm

LAST Step Rounding Answer

∴

r = 53211.2906mm

Instantaneous Radius for Cut given Rate of Increase of Wear-Land Formula Elements

Variables

Constants

Instantaneous Radius For Cut

Instantaneous Radius for Cut is the radius of the workpiece surface currently being machined.

Symbol: r

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Instantaneous Radius For Cut

Reference Cutting Velocity

Reference Cutting Velocity is the cutting velocity of the tool used in the reference machining Condition.

Symbol: V_ref

Measurement: SpeedUnit: m/s

Note: Value should be greater than 0.

Formulas to find Reference Cutting Velocity

Rate of Increase of Wear Land Width

Rate of Increase of Wear Land Width is the increase in the width of the region where wear occurs in a tool per unit time.

Symbol: W_r

Measurement: SpeedUnit: m/s

Note: Value should be greater than 0.

Formulas to find Rate of Increase of Wear Land Width

Reference Tool Life

Reference Tool Life is the Tool Life of the tool obtained in the reference machining condition.

Symbol: L_ref

Measurement: TimeUnit: min

Note: Value should be greater than 0.

Formulas to find Reference Tool Life

Maximum Wear Land Width

Maximum Wear Land Width is the maximum width of the region where wear occurs in a tool.

Symbol: W_max

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Maximum Wear Land Width

Taylor's Tool Life Exponent

Taylor's Tool Life Exponent is an experimental exponent that helps in quantifying the rate of tool wear.

Symbol: n

Measurement: NAUnit: Unitless

Note: Value should be less than 1.

Formulas to find Taylor's Tool Life Exponent

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.

Formulas to find Rotational Frequency of Spindle

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 Instantaneous Radius For Cut

Go Instantaneous Radius for Cut given Cutting Speed

r = \frac{V}{2 \cdot π \cdot ω s}

Go Instantaneous Radius for Cut

r = r o - ω s \cdot f \cdot t′

Other formulas in Instantaneous Radius category

Go Feed given Instantaneous Radius for Cut

f = \frac{r o - r}{ω s \cdot t′}

Go Workpiece Radius Ratio

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

How to Evaluate Instantaneous Radius for Cut given Rate of Increase of Wear-Land?

Instantaneous Radius for Cut given Rate of Increase of Wear-Land evaluator uses Instantaneous Radius For Cut = (Reference Cutting Velocity*(Rate of Increase of Wear Land Width*Reference Tool Life/Maximum Wear Land Width)^Taylor's Tool Life Exponent)/(2*pi*Rotational Frequency of Spindle) to evaluate the Instantaneous Radius For Cut, The Instantaneous Radius for Cut given Rate of Increase of Wear-Land is a method to determine the maximum radius of the workpiece that can be machined on a given spindle speed when Rate of Increase of Wear-Land is given. Instantaneous Radius For Cut is denoted by r symbol.

How to evaluate Instantaneous Radius for Cut given Rate of Increase of Wear-Land using this online evaluator? To use this online evaluator for Instantaneous Radius for Cut given Rate of Increase of Wear-Land, enter Reference Cutting Velocity (V_ref), Rate of Increase of Wear Land Width (W_r), Reference Tool Life (L_ref), Maximum Wear Land Width (W_max), Taylor's Tool Life Exponent (n) & Rotational Frequency of Spindle (ω_s) and hit the calculate button.

FAQs on Instantaneous Radius for Cut given Rate of Increase of Wear-Land

What is the formula to find Instantaneous Radius for Cut given Rate of Increase of Wear-Land?

The formula of Instantaneous Radius for Cut given Rate of Increase of Wear-Land is expressed as Instantaneous Radius For Cut = (Reference Cutting Velocity*(Rate of Increase of Wear Land Width*Reference Tool Life/Maximum Wear Land Width)^Taylor's Tool Life Exponent)/(2*pi*Rotational Frequency of Spindle). Here is an example- 6.9E+6 = (1050*(0.543*300/16.06691)^0.5)/(2*pi*10).

How to calculate Instantaneous Radius for Cut given Rate of Increase of Wear-Land?

With Reference Cutting Velocity (V_ref), Rate of Increase of Wear Land Width (W_r), Reference Tool Life (L_ref), Maximum Wear Land Width (W_max), Taylor's Tool Life Exponent (n) & Rotational Frequency of Spindle (ω_s) we can find Instantaneous Radius for Cut given Rate of Increase of Wear-Land using the formula - Instantaneous Radius For Cut = (Reference Cutting Velocity*(Rate of Increase of Wear Land Width*Reference Tool Life/Maximum Wear Land Width)^Taylor's Tool Life Exponent)/(2*pi*Rotational Frequency of Spindle). This formula also uses Archimedes' constant .

What are the other ways to Calculate Instantaneous Radius For Cut?

Here are the different ways to Calculate Instantaneous Radius For Cut-

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

Can the Instantaneous Radius for Cut given Rate of Increase of Wear-Land be negative?

No, the Instantaneous Radius for Cut given Rate of Increase of Wear-Land, measured in Length cannot be negative.

Which unit is used to measure Instantaneous Radius for Cut given Rate of Increase of Wear-Land?

Instantaneous Radius for Cut given Rate of Increase of Wear-Land is usually measured using the Millimeter[mm] for Length. Meter[mm], Kilometer[mm], Decimeter[mm] are the few other units in which Instantaneous Radius for Cut given Rate of Increase of Wear-Land can be measured.

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

​GoInstantaneous Radius for Cut given Cutting Speed Formula

​GoInstantaneous Radius for Cut Formula

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

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

Instantaneous Radius for Cut given Rate of Increase of Wear-Land Formula Elements

Other Formulas to find Instantaneous Radius For Cut

Other formulas in Instantaneous Radius category

How to Evaluate Instantaneous Radius for Cut given Rate of Increase of Wear-Land?

FAQs on Instantaneous Radius for Cut given Rate of Increase of Wear-Land

Variable Name

GoInstantaneous Radius for Cut given Cutting Speed Formula

GoInstantaneous Radius for Cut Formula