FormulaDen.com

Physics Chemistry Math Chemical Engineering Civil Electrical Electronics Electronics and Instrumentation Materials Science Mechanical Production Engineering Financial Health

Tool Life for minimum cost given Minimum Production Cost Formula

GoTool Life of One Tool for Minimum Machining Cost given Tool Changing Cost per Tool Formula

GoTool Life of One Tool for Minimum Machining Cost Formula

Fx Copy

LaTeX Copy

Tool Life is the period of time for which the cutting edge, affected by the cutting procedure, retains its cutting capacity between sharpening operations. Check FAQs

T = L \cdot ({(((\frac{C p}{R}) - t s) \cdot V \cdot \frac{1 - n}{K})}^{\frac{1}{n}})

T - Tool Life?L - Reference Tool Life?C_p - Production Cost of Each Component?R - Machining and Operating Rate?t_s - Setup Time?V - Reference Cutting Velocity?n - Taylor's Tool Life Exponent?K - Constant For Machining Condition?

Tool Life for minimum cost given Minimum Production Cost Example

With values

With units

Only example

Here is how the Tool Life for minimum cost given Minimum Production Cost equation looks like with Values.

Here is how the Tool Life for minimum cost given Minimum Production Cost equation looks like with Units.

Here is how the Tool Life for minimum cost given Minimum Production Cost equation looks like.

3000 = 60 \cdot ({(((\frac{5000}{7}) - 300) \cdot 0.76 \cdot \frac{1 - 0.125}{168.9469})}^{\frac{1}{0.125}})

3000s = 60s \cdot ({(((\frac{5000}{7}) - 300s) \cdot 0.76m/s \cdot \frac{1 - 0.125}{168.9469m})}^{\frac{1}{0.125}})

3000 = 60 \cdot ({(((\frac{5000}{7}) - 300) \cdot 0.76 \cdot \frac{1 - 0.125}{168.9469})}^{\frac{1}{0.125}})

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

Calculate

Recalculate

Solution

Copy

Reset

You are here -

Home » Engineering » Production Engineering » Metal Machining » Tool Life for minimum cost given Minimum Production Cost

Tool Life for minimum cost given Minimum Production Cost Solution

Follow our step by step solution on how to calculate Tool Life for minimum cost given Minimum Production Cost?

FIRST Step Consider the formula

T = L \cdot ({(((\frac{C p}{R}) - t s) \cdot V \cdot \frac{1 - n}{K})}^{\frac{1}{n}})

Next Step Substitute values of Variables

∴

T = 60s \cdot ({(((\frac{5000}{7}) - 300s) \cdot 0.76m/s \cdot \frac{1 - 0.125}{168.9469m})}^{\frac{1}{0.125}})

Next Step Prepare to Evaluate

∴

T = 60 \cdot ({(((\frac{5000}{7}) - 300) \cdot 0.76 \cdot \frac{1 - 0.125}{168.9469})}^{\frac{1}{0.125}})

Next Step Evaluate

∴

T = 3000.00000000003s

LAST Step Rounding Answer

∴

T = 3000s

Tool Life for minimum cost given Minimum Production Cost Formula Elements

Variables

Tool Life

Tool Life is the period of time for which the cutting edge, affected by the cutting procedure, retains its cutting capacity between sharpening operations.

Symbol: T

Measurement: TimeUnit: s

Note: Value should be greater than 0.

Reference Tool Life

Reference tool life refers to an estimated or theoretical lifespan of a cutting tool under ideal operating conditions.

Symbol: L

Measurement: TimeUnit: s

Note: Value should be greater than 0.

Production Cost of Each Component

Production cost of each component refers to the total expenses incurred in manufacturing a single component, taking into account all direct and indirect costs associated with the machining process.

Symbol: C_p

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Machining and Operating Rate

Machining and Operating Rate is the money charged for processing on and operating machines per unit time, including overheads.

Symbol: R

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Setup Time

Setup Time of each component is the time required to load/unload the workpiece and position the tool for production for one component.

Symbol: t_s

Measurement: TimeUnit: s

Note: Value should be greater than 0.

Reference Cutting Velocity

Reference cutting velocity refers to the ideal or theoretical speed at which the cutting tool moves relative to the workpiece material during the machining process.

Symbol: V

Measurement: SpeedUnit: m/s

Note: Value should be greater than 0.

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.

Constant For Machining Condition

Constant For Machining Condition can be regarded as the distance moved by the tool corner relative to the workpiece during a particular machining condition. It is usually measured in "Meter".

Symbol: K

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Credits

Created by Kumar Siddhant

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

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

Verified by Parul Keshav

National Institute of Technology (NIT), Srinagar

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

Other Formulas to find Tool Life

Go Tool Life of One Tool for Minimum Machining Cost given Tool Changing Cost per Tool

T = t q \cdot (C ct + C) \cdot \frac{1 - n}{n \cdot R}

Go Tool Life of One Tool for Minimum Machining Cost

T = t q \cdot (t c + (\frac{C}{R})) \cdot \frac{1 - n}{n}

Other formulas in Minimum Machining Cost category

Go Minimum Production Cost per Component

C p = R \cdot (t s + (K \cdot \frac{{(\frac{T}{L})}^{n}}{V \cdot (1 - n)}))

Go Machining and Operating Rate given Minimum Production Cost

R = \frac{C p}{t s + (K \cdot \frac{{(\frac{T}{L})}^{n}}{V \cdot (1 - n)})}

How to Evaluate Tool Life for minimum cost given Minimum Production Cost?

Tool Life for minimum cost given Minimum Production Cost evaluator uses Tool Life = Reference Tool Life*((((Production Cost of Each Component/Machining and Operating Rate)-Setup Time)*Reference Cutting Velocity*(1-Taylor's Tool Life Exponent)/Constant For Machining Condition)^(1/Taylor's Tool Life Exponent)) to evaluate the Tool Life, The Tool Life for minimum cost given Minimum Production Cost is a method to determine the time for which a tool can last when machining under a Constant Surface Speed condition when operating for the minimum cost of production. Tool Life is denoted by T symbol.

How to evaluate Tool Life for minimum cost given Minimum Production Cost using this online evaluator? To use this online evaluator for Tool Life for minimum cost given Minimum Production Cost, enter Reference Tool Life (L), Production Cost of Each Component (C_p), Machining and Operating Rate (R), Setup Time (t_s), Reference Cutting Velocity (V), Taylor's Tool Life Exponent (n) & Constant For Machining Condition (K) and hit the calculate button.

FAQs on Tool Life for minimum cost given Minimum Production Cost

What is the formula to find Tool Life for minimum cost given Minimum Production Cost?

The formula of Tool Life for minimum cost given Minimum Production Cost is expressed as Tool Life = Reference Tool Life*((((Production Cost of Each Component/Machining and Operating Rate)-Setup Time)*Reference Cutting Velocity*(1-Taylor's Tool Life Exponent)/Constant For Machining Condition)^(1/Taylor's Tool Life Exponent)). Here is an example- 3000.007 = 60*((((5000/7)-300)*0.76*(1-0.125)/168.946948749017)^(1/0.125)).

How to calculate Tool Life for minimum cost given Minimum Production Cost?

With Reference Tool Life (L), Production Cost of Each Component (C_p), Machining and Operating Rate (R), Setup Time (t_s), Reference Cutting Velocity (V), Taylor's Tool Life Exponent (n) & Constant For Machining Condition (K) we can find Tool Life for minimum cost given Minimum Production Cost using the formula - Tool Life = Reference Tool Life*((((Production Cost of Each Component/Machining and Operating Rate)-Setup Time)*Reference Cutting Velocity*(1-Taylor's Tool Life Exponent)/Constant For Machining Condition)^(1/Taylor's Tool Life Exponent)).

What are the other ways to Calculate Tool Life?

Here are the different ways to Calculate Tool Life-

Tool Life=Time Proportion*(Cost of Changing Each Tool+Cost of a Tool)*(1-Taylor's Tool Life Exponent)/(Taylor's Tool Life Exponent*Machining and Operating Rate)
Tool Life=Time Proportion*(Time to Change One Tool+(Cost of a Tool/Machining and Operating Rate))*(1-Taylor's Tool Life Exponent)/Taylor's Tool Life Exponent

Can the Tool Life for minimum cost given Minimum Production Cost be negative?

No, the Tool Life for minimum cost given Minimum Production Cost, measured in Time cannot be negative.

Which unit is used to measure Tool Life for minimum cost given Minimum Production Cost?

Tool Life for minimum cost given Minimum Production Cost is usually measured using the Second[s] for Time. Millisecond[s], Microsecond[s], Nanosecond[s] are the few other units in which Tool Life for minimum cost given Minimum Production Cost can be measured.

Spanish French German Russian Italian Portuguese Polish Dutch

Let Others Know

✖

Facebook

Twitter

Copied!

: Value
: Unit

Tool Life for minimum cost given Minimum Production Cost Formula

​GoTool Life of One Tool for Minimum Machining Cost given Tool Changing Cost per Tool Formula

​GoTool Life of One Tool for Minimum Machining Cost Formula

Tool Life for minimum cost given Minimum Production Cost Example

Tool Life for minimum cost given Minimum Production Cost Solution

Tool Life for minimum cost given Minimum Production Cost Formula Elements

Credits

Other Formulas to find Tool Life

Other formulas in Minimum Machining Cost category

How to Evaluate Tool Life for minimum cost given Minimum Production Cost?

FAQs on Tool Life for minimum cost given Minimum Production Cost

Variable Name

GoTool Life of One Tool for Minimum Machining Cost given Tool Changing Cost per Tool Formula

GoTool Life of One Tool for Minimum Machining Cost Formula