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

GoCost of One Tool given Cutting Velocity Formula

GoCost of One Tool given Tool Life 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}{1 - n}) \cdot ({(\frac{V ref}{V})}^{\frac{1}{n}})) - t c)

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

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

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Here is how the Cost of One Tool for Minimum Production Cost given cutting speed equation looks like with Values.

Here is how the Cost of One Tool for Minimum Production Cost given cutting speed equation looks like with Units.

Here is how the Cost of One Tool for Minimum Production Cost given cutting speed equation looks like.

48.5008 = 5 \cdot ((8400 \cdot (\frac{0.5408}{1 - 0.5408}) \cdot ({(\frac{2.9961}{420})}^{\frac{1}{0.5408}})) - 0.9)

48.5008 = 5 \cdot ((8400min \cdot (\frac{0.5408}{1 - 0.5408}) \cdot ({(\frac{2.9961m/min}{420m/min})}^{\frac{1}{0.5408}})) - 0.9min)

48.5008 = 5 \cdot ((8400 \cdot (\frac{0.5408}{1 - 0.5408}) \cdot ({(\frac{2.9961}{420})}^{\frac{1}{0.5408}})) - 0.9)

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

Follow our step by step solution on how to calculate Cost of One Tool for Minimum Production Cost given cutting speed?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

C t = 5 \cdot ((8400min \cdot (\frac{0.5408}{1 - 0.5408}) \cdot ({(\frac{2.9961m/min}{420m/min})}^{\frac{1}{0.5408}})) - 0.9min)

Next Step Convert Units

∴

C t = 5 \cdot ((504000s \cdot (\frac{0.5408}{1 - 0.5408}) \cdot ({(\frac{0.0499m/s}{7m/s})}^{\frac{1}{0.5408}})) - 54s)

Next Step Prepare to Evaluate

∴

C t = 5 \cdot ((504000 \cdot (\frac{0.5408}{1 - 0.5408}) \cdot ({(\frac{0.0499}{7})}^{\frac{1}{0.5408}})) - 54)

Next Step Evaluate

∴

C t = 48.5007584209938

LAST Step Rounding Answer

∴

C t = 48.5008

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

Formulas to find Cost of A Tool

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.

Formulas to find Machining And Operating Rate

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

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

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

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

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 Cost of A Tool

Go Cost of One Tool given Cutting Velocity

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

Go Cost of One Tool given Tool Life

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

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 for Minimum Production Cost given cutting speed?

Cost of One Tool for Minimum Production Cost given cutting speed evaluator uses 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) to evaluate the Cost of A Tool, The Cost of One Tool for Minimum Production Cost given cutting speed is a method to determine the maximum amount available to be spent on renewing the Machining Tool, such that the Total Production Cost is Minimum in reference to the Cutting Velocity of the Tool. Cost of A Tool is denoted by C_t symbol.

How to evaluate Cost of One Tool for Minimum Production Cost given cutting speed using this online evaluator? To use this online evaluator for Cost of One Tool for Minimum Production Cost given cutting speed, enter Machining And Operating Rate (M), Reference Tool Life (L_ref), Taylor's Tool Life Exponent (n), 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 for Minimum Production Cost given cutting speed

What is the formula to find Cost of One Tool for Minimum Production Cost given cutting speed?

The formula of Cost of One Tool for Minimum Production Cost given cutting speed is expressed as 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). Here is an example- 4.850076 = 5*((504000*(0.540818/(1-0.540818))*((0.0499342666666667/7)^(1/0.540818)))-54).

How to calculate Cost of One Tool for Minimum Production Cost given cutting speed?

With Machining And Operating Rate (M), Reference Tool Life (L_ref), Taylor's Tool Life Exponent (n), Reference Cutting Velocity (V_ref), Cutting Velocity (V) & Time to Change One Tool (t_c) we can find Cost of One Tool for Minimum Production Cost given cutting speed using the formula - 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).

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*((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)
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*Time to Change One Tool*((2*Taylor's Tool Life Exponent-1)/(1-Taylor's Tool Life Exponent))

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

​GoCost of One Tool given Cutting Velocity Formula

​GoCost of One Tool given Tool Life Formula

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

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

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

Other Formulas to find Cost of A Tool

Other formulas in Minimum Production Cost category

How to Evaluate Cost of One Tool for Minimum Production Cost given cutting speed?

FAQs on Cost of One Tool for Minimum Production Cost given cutting speed

Variable Name

GoCost of One Tool given Cutting Velocity Formula

GoCost of One Tool given Tool Life Formula