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Reference Cutting Velocity given Cutting Velocity Formula

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Reference Cutting Velocity is the Cutting Velocity of the tool used in the reference machining condition. Check FAQs

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

V_ref - Reference Cutting Velocity?V - 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?

Reference Cutting Velocity given Cutting Velocity Example

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Here is how the Reference Cutting Velocity given Cutting Velocity equation looks like with Values.

Here is how the Reference Cutting Velocity given Cutting Velocity equation looks like with Units.

Here is how the Reference Cutting Velocity given Cutting Velocity equation looks like.

2.7673 = \frac{420}{{(\frac{0.5408 \cdot 48 \cdot 8400}{(1 - 0.5408) \cdot (48 \cdot 0.9 + 48)})}^{0.5408}}

2.7673m/min = \frac{420m/min}{{(\frac{0.5408 \cdot 48 \cdot 8400min}{(1 - 0.5408) \cdot (48 \cdot 0.9min + 48)})}^{0.5408}}

2.7673 = \frac{420}{{(\frac{0.5408 \cdot 48 \cdot 8400}{(1 - 0.5408) \cdot (48 \cdot 0.9 + 48)})}^{0.5408}}

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Reference Cutting Velocity given Cutting Velocity Solution

Follow our step by step solution on how to calculate Reference Cutting Velocity given Cutting Velocity?

FIRST Step Consider the formula

V ref = \frac{V}{{(\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 ref = \frac{420m/min}{{(\frac{0.5408 \cdot 48 \cdot 8400min}{(1 - 0.5408) \cdot (48 \cdot 0.9min + 48)})}^{0.5408}}

Next Step Convert Units

∴

V ref = \frac{7m/s}{{(\frac{0.5408 \cdot 48 \cdot 504000s}{(1 - 0.5408) \cdot (48 \cdot 54s + 48)})}^{0.5408}}

Next Step Prepare to Evaluate

∴

V ref = \frac{7}{{(\frac{0.5408 \cdot 48 \cdot 504000}{(1 - 0.5408) \cdot (48 \cdot 54 + 48)})}^{0.5408}}

Next Step Evaluate

∴

V ref = 0.0461218274224771m/s

Next Step Convert to Output's Unit

∴

V ref = 2.76730964534863m/min

LAST Step Rounding Answer

∴

V ref = 2.7673m/min

Reference Cutting Velocity given Cutting Velocity Formula Elements

Variables

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

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 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 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 Reference Cutting Velocity given Cutting Velocity?

Reference Cutting Velocity given Cutting Velocity evaluator uses Reference Cutting Velocity = 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 Reference Cutting Velocity, The Reference Cutting Velocity given Cutting Velocity formula is a method to determine the optimal Cutting Velocity required for a given Batch Size in a reference machining condition to manufacture such that the Total Production Cost is minimum. Reference Cutting Velocity is denoted by V_ref symbol.

How to evaluate Reference Cutting Velocity given Cutting Velocity using this online evaluator? To use this online evaluator for Reference Cutting Velocity given Cutting Velocity, enter Cutting Velocity (V), 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 Reference Cutting Velocity given Cutting Velocity

What is the formula to find Reference Cutting Velocity given Cutting Velocity?

The formula of Reference Cutting Velocity given Cutting Velocity is expressed as Reference Cutting Velocity = 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- 136.91 = 7/(((0.540818*48*504000)/((1-0.540818)*(48*54+48)))^0.540818).

How to calculate Reference Cutting Velocity given Cutting Velocity?

With Cutting Velocity (V), 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 Reference Cutting Velocity given Cutting Velocity using the formula - Reference Cutting Velocity = 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 Reference Cutting Velocity given Cutting Velocity be negative?

No, the Reference Cutting Velocity given Cutting Velocity, measured in Speed cannot be negative.

Which unit is used to measure Reference Cutting Velocity given Cutting Velocity?

Reference Cutting Velocity given Cutting Velocity 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 Reference Cutting Velocity given Cutting Velocity can be measured.

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Reference Cutting Velocity given Cutting Velocity Formula

Reference Cutting Velocity given Cutting Velocity Example

Reference Cutting Velocity given Cutting Velocity Solution

Reference Cutting Velocity given Cutting Velocity Formula Elements

Other formulas in Minimum Production Cost category

How to Evaluate Reference Cutting Velocity given Cutting Velocity?

FAQs on Reference Cutting Velocity given Cutting Velocity

Variable Name