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Reference Tool Life given Minimum Production Cost Formula

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

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

L - Reference Tool Life?T - 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?

Reference Tool Life given Minimum Production Cost Example

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

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

Here is how the Reference Tool Life given Minimum Production Cost equation looks like.

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

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

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

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Reference Tool Life given Minimum Production Cost Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

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

Next Step Prepare to Evaluate

∴

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

Next Step Evaluate

∴

L = 59.9999999999993s

LAST Step Rounding Answer

∴

L = 60s

Reference Tool Life given Minimum Production Cost Formula Elements

Variables

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.

Formulas to find Reference Tool Life

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.

Formulas to find Tool Life

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.

Formulas to find Production Cost of Each Component

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.

Formulas to find Machining and Operating Rate

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.

Formulas to find Setup Time

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.

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

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.

Formulas to find Constant For Machining Condition

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 Reference Tool Life given Minimum Production Cost?

Reference Tool Life given Minimum Production Cost evaluator uses Reference Tool Life = 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 Reference Tool Life, The Reference Tool Life given Minimum Production Cost 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 Production Cost is minimum. Reference Tool Life is denoted by L symbol.

How to evaluate Reference Tool Life given Minimum Production Cost using this online evaluator? To use this online evaluator for Reference Tool Life given Minimum Production Cost, enter Tool Life (T), 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 Reference Tool Life given Minimum Production Cost

What is the formula to find Reference Tool Life given Minimum Production Cost?

The formula of Reference Tool Life given Minimum Production Cost is expressed as Reference Tool Life = 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- 60 = 3000/(((5000/7-300)*0.76*(1-0.125)/168.946948749017)^(1/0.125)).

How to calculate Reference Tool Life given Minimum Production Cost?

With Tool Life (T), 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 Reference Tool Life given Minimum Production Cost using the formula - Reference Tool Life = 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)).

Can the Reference Tool Life given Minimum Production Cost be negative?

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

Which unit is used to measure Reference Tool Life given Minimum Production Cost?

Reference Tool Life 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 Reference Tool Life given Minimum Production Cost can be measured.

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Reference Tool Life given Minimum Production Cost Formula

Reference Tool Life given Minimum Production Cost Example

Reference Tool Life given Minimum Production Cost Solution

Reference Tool Life given Minimum Production Cost Formula Elements

Other formulas in Minimum Machining Cost category

How to Evaluate Reference Tool Life given Minimum Production Cost?

FAQs on Reference Tool Life given Minimum Production Cost

Variable Name