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Cutting Velocity for Minimum Production Cost given Tool Changing Cost Formula

GoCutting Velocity for Minimum Production Cost Formula

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The Cutting Velocity is the tangential velocity at the periphery of the cutter or workpiece (whichever is rotating). Check FAQs

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

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

Cutting Velocity for Minimum Production Cost given Tool Changing Cost Example

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Here is how the Cutting Velocity for Minimum Production Cost given Tool Changing Cost equation looks like with Values.

Here is how the Cutting Velocity for Minimum Production Cost given Tool Changing Cost equation looks like with Units.

Here is how the Cutting Velocity for Minimum Production Cost given Tool Changing Cost equation looks like.

3591.8994 = 2.9961 \cdot {(\frac{0.5408 \cdot 48 \cdot 8400}{(1 - 0.5408) \cdot (9.8 + 48)})}^{0.5408}

3591.8994m/min = 2.9961m/min \cdot {(\frac{0.5408 \cdot 48 \cdot 8400min}{(1 - 0.5408) \cdot (9.8 + 48)})}^{0.5408}

3591.8994 = 2.9961 \cdot {(\frac{0.5408 \cdot 48 \cdot 8400}{(1 - 0.5408) \cdot (9.8 + 48)})}^{0.5408}

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Cutting Velocity for Minimum Production Cost given Tool Changing Cost Solution

Follow our step by step solution on how to calculate Cutting Velocity for Minimum Production Cost given Tool Changing Cost?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

V = 2.9961m/min \cdot {(\frac{0.5408 \cdot 48 \cdot 8400min}{(1 - 0.5408) \cdot (9.8 + 48)})}^{0.5408}

Next Step Convert Units

∴

V = 0.0499m/s \cdot {(\frac{0.5408 \cdot 48 \cdot 504000s}{(1 - 0.5408) \cdot (9.8 + 48)})}^{0.5408}

Next Step Prepare to Evaluate

∴

V = 0.0499 \cdot {(\frac{0.5408 \cdot 48 \cdot 504000}{(1 - 0.5408) \cdot (9.8 + 48)})}^{0.5408}

Next Step Evaluate

∴

V = 59.8649897686221m/s

Next Step Convert to Output's Unit

∴

V = 3591.89938611733m/min

LAST Step Rounding Answer

∴

V = 3591.8994m/min

Cutting Velocity for Minimum Production Cost given Tool Changing Cost Formula Elements

Variables

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

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

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

Other Formulas to find Cutting Velocity

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}

Other formulas in Minimum Production Cost category

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})

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 Cutting Velocity for Minimum Production Cost given Tool Changing Cost?

Cutting Velocity for Minimum Production Cost given Tool Changing Cost evaluator uses Cutting Velocity = Reference Cutting Velocity*((Taylor's Tool Life Exponent*Cost of A Tool*Reference Tool Life)/((1-Taylor's Tool Life Exponent)*(Cost of Changing Each Tool+Cost of A Tool)))^Taylor's Tool Life Exponent to evaluate the Cutting Velocity, The Cutting Velocity for Minimum Production Cost given Tool Changing Cost is a method to determine the Cutting Velocity required to operate on a workpiece such that the Cost of Production for a given Batch is Minimum. Cutting Velocity is denoted by V symbol.

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

FAQs on Cutting Velocity for Minimum Production Cost given Tool Changing Cost

What is the formula to find Cutting Velocity for Minimum Production Cost given Tool Changing Cost?

The formula of Cutting Velocity for Minimum Production Cost given Tool Changing Cost is expressed as Cutting Velocity = Reference Cutting Velocity*((Taylor's Tool Life Exponent*Cost of A Tool*Reference Tool Life)/((1-Taylor's Tool Life Exponent)*(Cost of Changing Each Tool+Cost of A Tool)))^Taylor's Tool Life Exponent. Here is an example- 215514 = 0.0499342666666667*((0.540818*48*504000)/((1-0.540818)*(9.8+48)))^0.540818.

How to calculate Cutting Velocity for Minimum Production Cost given Tool Changing Cost?

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

What are the other ways to Calculate Cutting Velocity?

Here are the different ways to Calculate Cutting Velocity-

Cutting Velocity=Reference Cutting Velocity*((Taylor's Tool Life Exponent*Cost of A Tool*Reference Tool Life)/((1-Taylor's Tool Life Exponent)*(Cost of A Tool*Time to Change One Tool+Cost of A Tool)))^Taylor's Tool Life Exponent

Can the Cutting Velocity for Minimum Production Cost given Tool Changing Cost be negative?

No, the Cutting Velocity for Minimum Production Cost given Tool Changing Cost, measured in Speed cannot be negative.

Which unit is used to measure Cutting Velocity for Minimum Production Cost given Tool Changing Cost?

Cutting Velocity for Minimum Production Cost given Tool Changing Cost is usually measured using the Meter per Minute[m/min] for Speed. Meter per Second[m/min], Meter per Hour[m/min], Kilometer per Hour[m/min] are the few other units in which Cutting Velocity for Minimum Production Cost given Tool Changing Cost can be measured.

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Cutting Velocity for Minimum Production Cost given Tool Changing Cost Formula

​GoCutting Velocity for Minimum Production Cost Formula

Cutting Velocity for Minimum Production Cost given Tool Changing Cost Example

Cutting Velocity for Minimum Production Cost given Tool Changing Cost Solution

Cutting Velocity for Minimum Production Cost given Tool Changing Cost Formula Elements

Other Formulas to find Cutting Velocity

Other formulas in Minimum Production Cost category

How to Evaluate Cutting Velocity for Minimum Production Cost given Tool Changing Cost?

FAQs on Cutting Velocity for Minimum Production Cost given Tool Changing Cost

Variable Name

GoCutting Velocity for Minimum Production Cost Formula