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Cost to change One Tool given Cutting Velocity Formula

GoCost to change One Tool given Tool Life Formula

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Cost of Changing Each Tool is the cost that arises due to the time taken by the operator to change one tool when one is paid by the hour. Check FAQs

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

C_ct - Cost of Changing Each Tool?C_t - Cost of A Tool?L_ref - Reference Tool Life?V - Cutting Velocity?V_ref - Reference Cutting Velocity?n - Taylor's Tool Life Exponent?

Cost to change One Tool given Cutting Velocity Example

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Here is how the Cost to change One Tool given Cutting Velocity equation looks like with Values.

Here is how the Cost to change One Tool given Cutting Velocity equation looks like with Units.

Here is how the Cost to change One Tool given Cutting Velocity equation looks like.

3009.6073 = (48 \cdot \frac{8400}{({(\frac{420}{2.9961})}^{\frac{1}{0.5408}}) \cdot \frac{1 - 0.5408}{0.5408}}) - 48

3009.6073 = (48 \cdot \frac{8400min}{({(\frac{420m/min}{2.9961m/min})}^{\frac{1}{0.5408}}) \cdot \frac{1 - 0.5408}{0.5408}}) - 48

3009.6073 = (48 \cdot \frac{8400}{({(\frac{420}{2.9961})}^{\frac{1}{0.5408}}) \cdot \frac{1 - 0.5408}{0.5408}}) - 48

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Cost to change One Tool given Cutting Velocity Solution

Follow our step by step solution on how to calculate Cost to change One Tool given Cutting Velocity?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

C ct = (48 \cdot \frac{8400min}{({(\frac{420m/min}{2.9961m/min})}^{\frac{1}{0.5408}}) \cdot \frac{1 - 0.5408}{0.5408}}) - 48

Next Step Convert Units

∴

C ct = (48 \cdot \frac{504000s}{({(\frac{7m/s}{0.0499m/s})}^{\frac{1}{0.5408}}) \cdot \frac{1 - 0.5408}{0.5408}}) - 48

Next Step Prepare to Evaluate

∴

C ct = (48 \cdot \frac{504000}{({(\frac{7}{0.0499})}^{\frac{1}{0.5408}}) \cdot \frac{1 - 0.5408}{0.5408}}) - 48

Next Step Evaluate

∴

C ct = 3009.60728084154

LAST Step Rounding Answer

∴

C ct = 3009.6073

Cost to change One Tool given Cutting Velocity Formula Elements

Variables

Cost of Changing Each Tool

Cost of Changing Each Tool is the cost that arises due to the time taken by the operator to change one tool when one is paid by the hour.

Symbol: C_ct

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Cost of Changing Each Tool

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

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

Other Formulas to find Cost of Changing Each Tool

Go Cost to change One Tool given Tool Life

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

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 Reference Tool Life given Cutting Velocity

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}

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})

How to Evaluate Cost to change One Tool given Cutting Velocity?

Cost to change One Tool given Cutting Velocity evaluator uses Cost of Changing Each Tool = (Cost of A Tool*Reference Tool Life/(((Cutting Velocity/Reference Cutting Velocity)^(1/Taylor's Tool Life Exponent))*(1-Taylor's Tool Life Exponent)/Taylor's Tool Life Exponent))-Cost of A Tool to evaluate the Cost of Changing Each Tool, Cost to change One Tool given Cutting Velocity is a method to determine the cost that arises due to the time taken by the operator in changing 1 Cutting Tool when he is paid by the hour maintaining conditions to Minimize the Total Production Cost. Cost of Changing Each Tool is denoted by C_ct symbol.

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

FAQs on Cost to change One Tool given Cutting Velocity

What is the formula to find Cost to change One Tool given Cutting Velocity?

The formula of Cost to change One Tool given Cutting Velocity is expressed as Cost of Changing Each Tool = (Cost of A Tool*Reference Tool Life/(((Cutting Velocity/Reference Cutting Velocity)^(1/Taylor's Tool Life Exponent))*(1-Taylor's Tool Life Exponent)/Taylor's Tool Life Exponent))-Cost of A Tool. Here is an example- 3009.607 = (48*504000/(((7/0.0499342666666667)^(1/0.540818))*(1-0.540818)/0.540818))-48.

How to calculate Cost to change One Tool given Cutting Velocity?

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

What are the other ways to Calculate Cost of Changing Each Tool?

Here are the different ways to Calculate Cost of Changing Each Tool-

Cost of Changing Each Tool=Cost of A Tool*(Tool Life*Taylor's Tool Life Exponent/(1-Taylor's Tool Life Exponent))-Cost of A Tool

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Cost to change One Tool given Cutting Velocity Formula

​GoCost to change One Tool given Tool Life Formula

Cost to change One Tool given Cutting Velocity Example

Cost to change One Tool given Cutting Velocity Solution

Cost to change One Tool given Cutting Velocity Formula Elements

Other Formulas to find Cost of Changing Each Tool

Other formulas in Minimum Production Cost category

How to Evaluate Cost to change One Tool given Cutting Velocity?

FAQs on Cost to change One Tool given Cutting Velocity

Variable Name

GoCost to change One Tool given Tool Life Formula