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Tool Life Exponent given Rate of Increase of Wear-Land Width Formula

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

n = \frac{\ln (\frac{V ref}{V})}{\ln (\frac{W max}{V ratio \cdot T ref})}

n - Taylor's Tool Life Exponent?V_ref - Reference Cutting Velocity?V - Cutting Velocity?W_max - Maximum Wear Land Width?V_ratio - Rate of Increase of Wear Land Width?T_ref - Reference Tool Life?

Tool Life Exponent given Rate of Increase of Wear-Land Width Example

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Here is how the Tool Life Exponent given Rate of Increase of Wear-Land Width equation looks like with Values.

Here is how the Tool Life Exponent given Rate of Increase of Wear-Land Width equation looks like with Units.

Here is how the Tool Life Exponent given Rate of Increase of Wear-Land Width equation looks like.

0.5 = \frac{\ln (\frac{5000}{8000})}{\ln (\frac{0.3125}{0.16 \cdot 5})}

0.5 = \frac{\ln (\frac{5000mm/min}{8000mm/min})}{\ln (\frac{0.3125mm}{0.16mm/min \cdot 5min})}

0.5 = \frac{\ln (\frac{5000}{8000})}{\ln (\frac{0.3125}{0.16 \cdot 5})}

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Metal Machining » fx Tool Life Exponent given Rate of Increase of Wear-Land Width

Tool Life Exponent given Rate of Increase of Wear-Land Width Solution

Follow our step by step solution on how to calculate Tool Life Exponent given Rate of Increase of Wear-Land Width?

FIRST Step Consider the formula

n = \frac{\ln (\frac{V ref}{V})}{\ln (\frac{W max}{V ratio \cdot T ref})}

Next Step Substitute values of Variables

∴

n = \frac{\ln (\frac{5000mm/min}{8000mm/min})}{\ln (\frac{0.3125mm}{0.16mm/min \cdot 5min})}

Next Step Convert Units

∴

n = \frac{\ln (\frac{0.0833m/s}{0.1333m/s})}{\ln (\frac{0.0003m}{2.7E-6m/s \cdot 300s})}

Next Step Prepare to Evaluate

∴

n = \frac{\ln (\frac{0.0833}{0.1333})}{\ln (\frac{0.0003}{2.7E-6 \cdot 300})}

Next Step Evaluate

∴

n = 0.499999999999997

LAST Step Rounding Answer

∴

n = 0.5

Tool Life Exponent given Rate of Increase of Wear-Land Width Formula Elements

Variables

Functions

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

Open Variable

Reference Cutting Velocity

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

Symbol: V_ref

Measurement: SpeedUnit: mm/min

Note: Value should be greater than 0.

Formulas to find Reference Cutting Velocity

Open Variable

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

Open Variable

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

Open Variable

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: V_ratio

Measurement: SpeedUnit: mm/min

Note: Value should be greater than 0.

Formulas to find Rate of Increase of Wear Land Width

Open Variable

Reference Tool Life

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

Symbol: T_ref

Measurement: TimeUnit: min

Note: Value should be greater than 0.

Formulas to find Reference Tool Life

Open Variable

ln

The natural logarithm, also known as the logarithm to the base e, is the inverse function of the natural exponential function.

Syntax: ln(Number)

Other formulas in Wear Land category

Go Maximum Wear-Land Width

W max = L w \cdot \frac{T}{t m}

Go Increase in Wear-Land Width per Component

L w = W max \cdot \frac{t m}{T}

Go Machining Time given Maximum Wear-Land Width

t m = L w \cdot \frac{T}{W max}

Go Maximum Wear-Land Width given Rate of Increase of Wear-Land Width

W max = V ratio \cdot T ref \cdot ({(\frac{V ref}{V})}^{\frac{1}{n}})

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How to Evaluate Tool Life Exponent given Rate of Increase of Wear-Land Width?

Tool Life Exponent given Rate of Increase of Wear-Land Width evaluator uses Taylor's Tool Life Exponent = ln(Reference Cutting Velocity/Cutting Velocity)/ln(Maximum Wear Land Width/(Rate of Increase of Wear Land Width*Reference Tool Life)) to evaluate the Taylor's Tool Life Exponent, The Tool Life Exponent given Rate of Increase of Wear-Land Width is a method to determine the Tool Life for the Current condition when Rate of Increase of Wear-Land Width is given. Taylor's Tool Life Exponent is denoted by n symbol.

How to evaluate Tool Life Exponent given Rate of Increase of Wear-Land Width using this online evaluator? To use this online evaluator for Tool Life Exponent given Rate of Increase of Wear-Land Width, enter Reference Cutting Velocity (V_ref), Cutting Velocity (V), Maximum Wear Land Width (W_max), Rate of Increase of Wear Land Width (V_ratio) & Reference Tool Life (T_ref) and hit the calculate button.

FAQs on Tool Life Exponent given Rate of Increase of Wear-Land Width

What is the formula to find Tool Life Exponent given Rate of Increase of Wear-Land Width?

The formula of Tool Life Exponent given Rate of Increase of Wear-Land Width is expressed as Taylor's Tool Life Exponent = ln(Reference Cutting Velocity/Cutting Velocity)/ln(Maximum Wear Land Width/(Rate of Increase of Wear Land Width*Reference Tool Life)). Here is an example- 0.5 = ln(0.0833333333333333/0.133333333333333)/ln(0.0003125/(2.66666666666667E-06*300)).

How to calculate Tool Life Exponent given Rate of Increase of Wear-Land Width?

With Reference Cutting Velocity (V_ref), Cutting Velocity (V), Maximum Wear Land Width (W_max), Rate of Increase of Wear Land Width (V_ratio) & Reference Tool Life (T_ref) we can find Tool Life Exponent given Rate of Increase of Wear-Land Width using the formula - Taylor's Tool Life Exponent = ln(Reference Cutting Velocity/Cutting Velocity)/ln(Maximum Wear Land Width/(Rate of Increase of Wear Land Width*Reference Tool Life)). This formula also uses Natural Logarithm (ln) function(s).

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