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Cutting Velocity for Minimum Production Cost Formula

GoCutting Velocity for Minimum Production Cost given Tool Changing 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 t \cdot t c + 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?t_c - Time to Change One Tool?

Cutting Velocity for Minimum Production Cost Example

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With units

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

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

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

454.7173 = 2.9961 \cdot {(\frac{0.5408 \cdot 48 \cdot 8400}{(1 - 0.5408) \cdot (48 \cdot 0.9 + 48)})}^{0.5408}

454.7173m/min = 2.9961m/min \cdot {(\frac{0.5408 \cdot 48 \cdot 8400min}{(1 - 0.5408) \cdot (48 \cdot 0.9min + 48)})}^{0.5408}

454.7173 = 2.9961 \cdot {(\frac{0.5408 \cdot 48 \cdot 8400}{(1 - 0.5408) \cdot (48 \cdot 0.9 + 48)})}^{0.5408}

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Cutting Velocity for Minimum Production Cost Solution

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

FIRST Step Consider the formula

V = V ref \cdot {(\frac{n \cdot C t \cdot L ref}{(1 - n) \cdot (C t \cdot t c + 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 (48 \cdot 0.9min + 48)})}^{0.5408}

Next Step Convert Units

∴

V = 0.0499m/s \cdot {(\frac{0.5408 \cdot 48 \cdot 504000s}{(1 - 0.5408) \cdot (48 \cdot 54s + 48)})}^{0.5408}

Next Step Prepare to Evaluate

∴

V = 0.0499 \cdot {(\frac{0.5408 \cdot 48 \cdot 504000}{(1 - 0.5408) \cdot (48 \cdot 54 + 48)})}^{0.5408}

Next Step Evaluate

∴

V = 7.57862136434606m/s

Next Step Convert to Output's Unit

∴

V = 454.717281860764m/min

LAST Step Rounding Answer

∴

V = 454.7173m/min

Cutting Velocity for Minimum Production 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

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 to find Cutting Velocity

Go Cutting Velocity for Minimum Production Cost given Tool Changing Cost

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

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

FAQs on Cutting Velocity for Minimum Production Cost

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

The formula of Cutting Velocity for Minimum Production 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 A Tool*Time to Change One Tool+Cost of A Tool)))^Taylor's Tool Life Exponent. Here is an example- 27283.04 = 0.0499342666666667*((0.540818*48*504000)/((1-0.540818)*(48*54+48)))^0.540818.

How to calculate Cutting Velocity for Minimum Production Cost?

With Reference Cutting Velocity (V_ref), Taylor's Tool Life Exponent (n), Cost of A Tool (C_t), Reference Tool Life (L_ref) & Time to Change One Tool (t_c) we can find Cutting Velocity for Minimum Production 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 A Tool*Time to Change One 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 Changing Each Tool+Cost of A Tool)))^Taylor's Tool Life Exponent

Can the Cutting Velocity for Minimum Production Cost be negative?

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

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

Cutting Velocity for Minimum Production 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 can be measured.

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Cutting Velocity for Minimum Production Cost Formula

​GoCutting Velocity for Minimum Production Cost given Tool Changing Cost Formula

Cutting Velocity for Minimum Production Cost Example

Cutting Velocity for Minimum Production Cost Solution

Cutting Velocity for Minimum Production 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?

FAQs on Cutting Velocity for Minimum Production Cost

Variable Name

GoCutting Velocity for Minimum Production Cost given Tool Changing Cost Formula