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Cost of One Tool given Cutting Velocity Formula

GoCost of One Tool given Tool Life Formula

GoCost of One Tool for Minimum Production Cost given cutting speed Formula

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Cost of A Tool is simply the cost of one tool being used for machining. Check FAQs

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

C_t - Cost of A Tool?M - Machining And Operating Rate?L_ref - Reference Tool Life?n_h - Taylor's Tool Life Exponent For Hard Material?V_ref - Reference Cutting Velocity?V - Cutting Velocity?t_c - Time to Change One Tool?

Cost of One Tool given Cutting Velocity Example

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

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

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

292416.181 = 5 \cdot ((8400 \cdot (\frac{1.55}{1.55 - 1}) \cdot {(\frac{2.9961}{420})}^{\frac{1}{1.55}}) - 0.9)

292416.181 = 5 \cdot ((8400min \cdot (\frac{1.55}{1.55 - 1}) \cdot {(\frac{2.9961m/min}{420m/min})}^{\frac{1}{1.55}}) - 0.9min)

292416.181 = 5 \cdot ((8400 \cdot (\frac{1.55}{1.55 - 1}) \cdot {(\frac{2.9961}{420})}^{\frac{1}{1.55}}) - 0.9)

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Home » Engineering » Production Engineering » Metal Machining » Cost of One Tool given Cutting Velocity

Cost of One Tool given Cutting Velocity Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

C t = 5 \cdot ((8400min \cdot (\frac{1.55}{1.55 - 1}) \cdot {(\frac{2.9961m/min}{420m/min})}^{\frac{1}{1.55}}) - 0.9min)

Next Step Convert Units

∴

C t = 5 \cdot ((504000s \cdot (\frac{1.55}{1.55 - 1}) \cdot {(\frac{0.0499m/s}{7m/s})}^{\frac{1}{1.55}}) - 54s)

Next Step Prepare to Evaluate

∴

C t = 5 \cdot ((504000 \cdot (\frac{1.55}{1.55 - 1}) \cdot {(\frac{0.0499}{7})}^{\frac{1}{1.55}}) - 54)

Next Step Evaluate

∴

C t = 292416.181007095

LAST Step Rounding Answer

∴

C t = 292416.181

Cost of One Tool given Cutting Velocity Formula Elements

Variables

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.

Machining And Operating Rate

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

Symbol: M

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

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.

Taylor's Tool Life Exponent For Hard Material

Taylor's Tool Life Exponent For Hard Material is a parameter used in machining operations to describe the relationship between cutting speed and tool life.

Symbol: n_h

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

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.

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.

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.

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 Cost of A Tool

Go Cost of One Tool given Tool Life

C t = M \cdot t c \cdot (\frac{2 \cdot n - 1}{1 - n})

Go Cost of One Tool for Minimum Production Cost given cutting speed

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

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}}

How to Evaluate Cost of One Tool given Cutting Velocity?

Cost of One Tool given Cutting Velocity evaluator uses Cost of A Tool = Machining And Operating Rate*((Reference Tool Life*(Taylor's Tool Life Exponent For Hard Material/(Taylor's Tool Life Exponent For Hard Material-1))*(Reference Cutting Velocity/Cutting Velocity)^(1/Taylor's Tool Life Exponent For Hard Material))-Time to Change One Tool) to evaluate the Cost of A Tool, The Cost of One Tool given Cutting Velocity is a method to determine the maximum amount available to be spent on renewing the Machining Tool for the production of a batch of components, such that the Total Production Cost is Minimum. Cost of A Tool is denoted by C_t symbol.

How to evaluate Cost of One Tool given Cutting Velocity using this online evaluator? To use this online evaluator for Cost of One Tool given Cutting Velocity, enter Machining And Operating Rate (M), Reference Tool Life (L_ref), Taylor's Tool Life Exponent For Hard Material (n_h), Reference Cutting Velocity (V_ref), Cutting Velocity (V) & Time to Change One Tool (t_c) and hit the calculate button.

FAQs on Cost of One Tool given Cutting Velocity

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

The formula of Cost of One Tool given Cutting Velocity is expressed as Cost of A Tool = Machining And Operating Rate*((Reference Tool Life*(Taylor's Tool Life Exponent For Hard Material/(Taylor's Tool Life Exponent For Hard Material-1))*(Reference Cutting Velocity/Cutting Velocity)^(1/Taylor's Tool Life Exponent For Hard Material))-Time to Change One Tool). Here is an example- 292416.2 = 5*((504000*(1.55/(1.55-1))*(0.0499342666666667/7)^(1/1.55))-54).

How to calculate Cost of One Tool given Cutting Velocity?

With Machining And Operating Rate (M), Reference Tool Life (L_ref), Taylor's Tool Life Exponent For Hard Material (n_h), Reference Cutting Velocity (V_ref), Cutting Velocity (V) & Time to Change One Tool (t_c) we can find Cost of One Tool given Cutting Velocity using the formula - Cost of A Tool = Machining And Operating Rate*((Reference Tool Life*(Taylor's Tool Life Exponent For Hard Material/(Taylor's Tool Life Exponent For Hard Material-1))*(Reference Cutting Velocity/Cutting Velocity)^(1/Taylor's Tool Life Exponent For Hard Material))-Time to Change One Tool).

What are the other ways to Calculate Cost of A Tool?

Here are the different ways to Calculate Cost of A Tool-

Cost of A Tool=Machining And Operating Rate*Time to Change One Tool*((2*Taylor's Tool Life Exponent-1)/(1-Taylor's Tool Life Exponent))
Cost of A Tool=Machining And Operating Rate*((Reference Tool Life*(Taylor's Tool Life Exponent/(1-Taylor's Tool Life Exponent))*((Reference Cutting Velocity/Cutting Velocity)^(1/Taylor's Tool Life Exponent)))-Time to Change One Tool)
Cost of A Tool=Machining And Operating Rate*Time to Change One Tool*((2*Taylor's Tool Life Exponent-1)/(1-Taylor's Tool Life Exponent))

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: Unit

Cost of One Tool given Cutting Velocity Formula

​GoCost of One Tool given Tool Life Formula

​GoCost of One Tool for Minimum Production Cost given cutting speed Formula

Cost of One Tool given Cutting Velocity Example

Cost of One Tool given Cutting Velocity Solution

Cost of One Tool given Cutting Velocity Formula Elements

Credits

Other Formulas to find Cost of A Tool

Other formulas in Minimum Production Cost category

How to Evaluate Cost of One Tool given Cutting Velocity?

FAQs on Cost of One Tool given Cutting Velocity

Variable Name

GoCost of One Tool given Tool Life Formula

GoCost of One Tool for Minimum Production Cost given cutting speed Formula