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Reference Tool Life given Cutting Velocity Formula

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

L ref = {(\frac{V}{V ref})}^{\frac{1}{n}} \cdot (1 - n) \cdot \frac{C t \cdot t c + C t}{n \cdot C t}

L_ref - Reference Tool Life?V - Cutting Velocity?V_ref - Reference Cutting Velocity?n - Taylor's Tool Life Exponent?C_t - Cost of A Tool?t_c - Time to Change One Tool?

Reference Tool Life given Cutting Velocity Example

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Here is how the Reference Tool Life given Cutting Velocity equation looks like with Values.

Here is how the Reference Tool Life given Cutting Velocity equation looks like with Units.

Here is how the Reference Tool Life given Cutting Velocity equation looks like.

7252.73 = {(\frac{420}{2.9961})}^{\frac{1}{0.5408}} \cdot (1 - 0.5408) \cdot \frac{48 \cdot 0.9 + 48}{0.5408 \cdot 48}

7252.73min = {(\frac{420m/min}{2.9961m/min})}^{\frac{1}{0.5408}} \cdot (1 - 0.5408) \cdot \frac{48 \cdot 0.9min + 48}{0.5408 \cdot 48}

7252.73 = {(\frac{420}{2.9961})}^{\frac{1}{0.5408}} \cdot (1 - 0.5408) \cdot \frac{48 \cdot 0.9 + 48}{0.5408 \cdot 48}

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Reference Tool Life given Cutting Velocity Solution

Follow our step by step solution on how to calculate Reference Tool Life given Cutting Velocity?

FIRST Step Consider the formula

L ref = {(\frac{V}{V ref})}^{\frac{1}{n}} \cdot (1 - n) \cdot \frac{C t \cdot t c + C t}{n \cdot C t}

Next Step Substitute values of Variables

∴

L ref = {(\frac{420m/min}{2.9961m/min})}^{\frac{1}{0.5408}} \cdot (1 - 0.5408) \cdot \frac{48 \cdot 0.9min + 48}{0.5408 \cdot 48}

Next Step Convert Units

∴

L ref = {(\frac{7m/s}{0.0499m/s})}^{\frac{1}{0.5408}} \cdot (1 - 0.5408) \cdot \frac{48 \cdot 54s + 48}{0.5408 \cdot 48}

Next Step Prepare to Evaluate

∴

L ref = {(\frac{7}{0.0499})}^{\frac{1}{0.5408}} \cdot (1 - 0.5408) \cdot \frac{48 \cdot 54 + 48}{0.5408 \cdot 48}

Next Step Evaluate

∴

L ref = 435163.798940782s

Next Step Convert to Output's Unit

∴

L ref = 7252.72998234637min

LAST Step Rounding Answer

∴

L ref = 7252.73min

Reference Tool Life given Cutting Velocity Formula Elements

Variables

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

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/min

Note: Value should be greater than 0.

Formulas to find Cutting Velocity

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/min

Note: Value should be greater than 0.

Formulas to find Reference Cutting Velocity

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

Cost of A Tool

Cost of A Tool is simply the cost of one tool being used for machining.

Symbol: C_t

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Cost of A Tool

Time to Change One Tool

Time to Change One Tool is the measure of time it takes to change one tool during machining.

Symbol: t_c

Measurement: TimeUnit: min

Note: Value should be greater than 0.

Formulas to find Time to Change One Tool

Other formulas in Minimum Production Cost category

Go Cutting Velocity for Minimum Production Cost

V = V ref \cdot {(\frac{n \cdot C t \cdot L ref}{(1 - n) \cdot (C t \cdot t c + C t)})}^{n}

Go Reference Cutting Velocity given Cutting Velocity

V ref = \frac{V}{{(\frac{n \cdot C t \cdot L ref}{(1 - n) \cdot (C t \cdot t c + C t)})}^{n}}

Go Machining and Operating Rate using Minimum Production Cost

M = (\frac{C t}{(L ref \cdot (\frac{n h}{n h - 1}) \cdot {(\frac{V ref}{V})}^{\frac{1}{n h}}) - t c})

Go Tool Changing Time for each Tool given Cutting Velocity

t c = \frac{(C t \cdot \frac{L ref}{{(\frac{V}{V ref})}^{\frac{1}{n}} \cdot \frac{1 - n}{n}}) - C t}{C t}

How to Evaluate Reference Tool Life given Cutting Velocity?

Reference Tool Life given Cutting Velocity evaluator uses Reference Tool Life = (Cutting Velocity/Reference Cutting Velocity)^(1/Taylor's Tool Life Exponent)*(1-Taylor's Tool Life Exponent)*(Cost of A Tool*Time to Change One Tool+Cost of A Tool)/(Taylor's Tool Life Exponent*Cost of A Tool) to evaluate the Reference Tool Life, The Reference Tool Life given Cutting Velocity is a method to determine the optimal Tool Sharpening period required in reference machining condition to manufacture a given batch of components such that The Total Production Cost is minimum. Reference Tool Life is denoted by L_ref symbol.

How to evaluate Reference Tool Life given Cutting Velocity using this online evaluator? To use this online evaluator for Reference Tool Life given Cutting Velocity, enter Cutting Velocity (V), Reference Cutting Velocity (V_ref), Taylor's Tool Life Exponent (n), Cost of A Tool (C_t) & Time to Change One Tool (t_c) and hit the calculate button.

FAQs on Reference Tool Life given Cutting Velocity

What is the formula to find Reference Tool Life given Cutting Velocity?

The formula of Reference Tool Life given Cutting Velocity is expressed as Reference Tool Life = (Cutting Velocity/Reference Cutting Velocity)^(1/Taylor's Tool Life Exponent)*(1-Taylor's Tool Life Exponent)*(Cost of A Tool*Time to Change One Tool+Cost of A Tool)/(Taylor's Tool Life Exponent*Cost of A Tool). Here is an example- 120.8788 = (7/0.0499342666666667)^(1/0.540818)*(1-0.540818)*(48*54+48)/(0.540818*48).

How to calculate Reference Tool Life given Cutting Velocity?

With Cutting Velocity (V), Reference Cutting Velocity (V_ref), Taylor's Tool Life Exponent (n), Cost of A Tool (C_t) & Time to Change One Tool (t_c) we can find Reference Tool Life given Cutting Velocity using the formula - Reference Tool Life = (Cutting Velocity/Reference Cutting Velocity)^(1/Taylor's Tool Life Exponent)*(1-Taylor's Tool Life Exponent)*(Cost of A Tool*Time to Change One Tool+Cost of A Tool)/(Taylor's Tool Life Exponent*Cost of A Tool).

Can the Reference Tool Life given Cutting Velocity be negative?

No, the Reference Tool Life given Cutting Velocity, measured in Time cannot be negative.

Which unit is used to measure Reference Tool Life given Cutting Velocity?

Reference Tool Life given Cutting Velocity is usually measured using the Minute[min] for Time. Second[min], Millisecond[min], Microsecond[min] are the few other units in which Reference Tool Life given Cutting Velocity can be measured.

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Reference Tool Life given Cutting Velocity Formula

Reference Tool Life given Cutting Velocity Example

Reference Tool Life given Cutting Velocity Solution

Reference Tool Life given Cutting Velocity Formula Elements

Other formulas in Minimum Production Cost category

How to Evaluate Reference Tool Life given Cutting Velocity?

FAQs on Reference Tool Life given Cutting Velocity

Variable Name