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Taylor's Exponent given Cutting Speed for Constant-Cutting-Speed Operation Formula

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Taylor's Tool Life Exponent is a parameter used in tool life equations to describe the relationship between cutting speed and tool life in metal machining. Check FAQs

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

n - Taylor's Tool Life Exponent?V - Cutting Velocity?V_ref - Reference Cutting Velocity?T_ref - Reference Tool Life?L - Tool Life?Q - Time Proportion of Cutting Edge?

Taylor's Exponent given Cutting Speed for Constant-Cutting-Speed Operation Example

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With units

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Here is how the Taylor's Exponent given Cutting Speed for Constant-Cutting-Speed Operation equation looks like with Values.

Here is how the Taylor's Exponent given Cutting Speed for Constant-Cutting-Speed Operation equation looks like with Units.

Here is how the Taylor's Exponent given Cutting Speed for Constant-Cutting-Speed Operation equation looks like.

0.5129 = \frac{\ln (\frac{8000}{5000})}{\ln (\frac{5}{50 \cdot 0.04})}

0.5129 = \frac{\ln (\frac{8000mm/min}{5000mm/min})}{\ln (\frac{5min}{50min \cdot 0.04})}

0.5129 = \frac{\ln (\frac{8000}{5000})}{\ln (\frac{5}{50 \cdot 0.04})}

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Taylor's Exponent given Cutting Speed for Constant-Cutting-Speed Operation Solution

Follow our step by step solution on how to calculate Taylor's Exponent given Cutting Speed for Constant-Cutting-Speed Operation?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

n = \frac{\ln (\frac{8000mm/min}{5000mm/min})}{\ln (\frac{5min}{50min \cdot 0.04})}

Next Step Convert Units

∴

n = \frac{\ln (\frac{0.1333m/s}{0.0833m/s})}{\ln (\frac{300s}{3000s \cdot 0.04})}

Next Step Prepare to Evaluate

∴

n = \frac{\ln (\frac{0.1333}{0.0833})}{\ln (\frac{300}{3000 \cdot 0.04})}

Next Step Evaluate

∴

n = 0.512941594732058

LAST Step Rounding Answer

∴

n = 0.5129

Taylor's Exponent given Cutting Speed for Constant-Cutting-Speed Operation Formula Elements

Variables

Functions

Taylor's Tool Life Exponent

Taylor's Tool Life Exponent is a parameter used in tool life equations to describe the relationship between cutting speed and tool life in metal machining.

Symbol: n

Measurement: NAUnit: Unitless

Note: Value should be between 0 to 1.

Formulas to find Taylor's Tool Life Exponent

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

Reference Cutting Velocity

Reference Cutting Velocity refers to a standard cutting speed used as a baseline or reference point for selecting appropriate cutting speeds for specific machining operations.

Symbol: V_ref

Measurement: SpeedUnit: mm/min

Note: Value should be greater than 0.

Formulas to find Reference Cutting Velocity

Open Variable

Reference Tool Life

Reference Tool Life refers to a standard or predetermined lifespan used as a baseline for estimating the expected durability of cutting tools under specific machining conditions.

Symbol: T_ref

Measurement: TimeUnit: min

Note: Value should be greater than 0.

Formulas to find Reference Tool Life

Open Variable

Tool Life

Tool Life refers to the duration or number of components machined before a cutting tool becomes no longer capable of maintaining the desired machining quality or performance standards.

Symbol: L

Measurement: TimeUnit: min

Note: Value should be greater than 0.

Formulas to find Tool Life

Open Variable

Time Proportion of Cutting Edge

Time Proportion of Cutting Edge is the duration during a machining operation that a specific portion of the cutting edge of the tool is actively engaged in removing material from the workpiece.

Symbol: Q

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Time Proportion of Cutting Edge

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 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 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 Time for Facing given Instantaneous Cutting Speed

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

See More

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How to Evaluate Taylor's Exponent given Cutting Speed for Constant-Cutting-Speed Operation?

Taylor's Exponent given Cutting Speed for Constant-Cutting-Speed Operation evaluator uses Taylor's Tool Life Exponent = ln(Cutting Velocity/Reference Cutting Velocity)/ln(Reference Tool Life/(Tool Life*Time Proportion of Cutting Edge)) to evaluate the Taylor's Tool Life Exponent, The Taylor's Exponent given Cutting Speed for Constant-Cutting-Speed Operation also known as Taylor's tool life exponent, is a parameter used in tool life equations to model the relationship between tool life and cutting speed for a constant-cutting-speed operation. Taylor's exponent is typically determined experimentally for a specific combination of cutting parameters, tooling, and material being machined. Taylor's Tool Life Exponent is denoted by n symbol.

How to evaluate Taylor's Exponent given Cutting Speed for Constant-Cutting-Speed Operation using this online evaluator? To use this online evaluator for Taylor's Exponent given Cutting Speed for Constant-Cutting-Speed Operation, enter Cutting Velocity (V), Reference Cutting Velocity (V_ref), Reference Tool Life (T_ref), Tool Life (L) & Time Proportion of Cutting Edge (Q) and hit the calculate button.

FAQs on Taylor's Exponent given Cutting Speed for Constant-Cutting-Speed Operation

What is the formula to find Taylor's Exponent given Cutting Speed for Constant-Cutting-Speed Operation?

The formula of Taylor's Exponent given Cutting Speed for Constant-Cutting-Speed Operation is expressed as Taylor's Tool Life Exponent = ln(Cutting Velocity/Reference Cutting Velocity)/ln(Reference Tool Life/(Tool Life*Time Proportion of Cutting Edge)). Here is an example- 0.057595 = ln(0.133333333333333/0.0833333333333333)/ln(300/(3000*0.04)).

How to calculate Taylor's Exponent given Cutting Speed for Constant-Cutting-Speed Operation?

With Cutting Velocity (V), Reference Cutting Velocity (V_ref), Reference Tool Life (T_ref), Tool Life (L) & Time Proportion of Cutting Edge (Q) we can find Taylor's Exponent given Cutting Speed for Constant-Cutting-Speed Operation using the formula - Taylor's Tool Life Exponent = ln(Cutting Velocity/Reference Cutting Velocity)/ln(Reference Tool Life/(Tool Life*Time Proportion of Cutting Edge)). This formula also uses Natural Logarithm (ln) function(s).

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