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Reference Cutting Speed given Production Cost per Component 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{\frac{K}{L ref} \cdot (M \cdot t c + C t) \cdot (V^{\frac{1 - n}{n}})}{C p - M \cdot (NPT + \frac{K}{V})})}^{n}

V_ref - Reference Cutting Velocity?K - Constant For Machining Condition?L_ref - Reference Tool Life?M - Machining And Operating Rate?t_c - Time to Change One Tool?C_t - Cost of A Tool?V - Cutting Velocity?n - Taylors Tool Life Exponent?C_p - Production Cost of Each Component?NPT - Non-Productive Time?

Reference Cutting Speed given Production Cost per Component Example

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Here is how the Reference Cutting Speed given Production Cost per Component equation looks like with Values.

Here is how the Reference Cutting Speed given Production Cost per Component equation looks like with Units.

Here is how the Reference Cutting Speed given Production Cost per Component equation looks like.

0.76 = {(\frac{\frac{203.0681}{2} \cdot (0.0028 \cdot 5 + 100) \cdot ({0.28}^{\frac{1 - 0.125}{0.125}})}{5.6553 - 0.0028 \cdot (20 + \frac{203.0681}{0.28})})}^{0.125}

0.76m/s = {(\frac{\frac{203.0681m}{2min} \cdot (0.0028 \cdot 5min + 100) \cdot ({0.28m/s}^{\frac{1 - 0.125}{0.125}})}{5.6553 - 0.0028 \cdot (20min + \frac{203.0681m}{0.28m/s})})}^{0.125}

0.76 = {(\frac{\frac{203.0681}{2} \cdot (0.0028 \cdot 5 + 100) \cdot ({0.28}^{\frac{1 - 0.125}{0.125}})}{5.6553 - 0.0028 \cdot (20 + \frac{203.0681}{0.28})})}^{0.125}

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Reference Cutting Speed given Production Cost per Component Solution

Follow our step by step solution on how to calculate Reference Cutting Speed given Production Cost per Component?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

V ref = {(\frac{\frac{203.0681m}{2min} \cdot (0.0028 \cdot 5min + 100) \cdot ({0.28m/s}^{\frac{1 - 0.125}{0.125}})}{5.6553 - 0.0028 \cdot (20min + \frac{203.0681m}{0.28m/s})})}^{0.125}

Next Step Convert Units

∴

V ref = {(\frac{\frac{203.0681m}{120s} \cdot (0.0028 \cdot 300s + 100) \cdot ({0.28m/s}^{\frac{1 - 0.125}{0.125}})}{5.6553 - 0.0028 \cdot (1200s + \frac{203.0681m}{0.28m/s})})}^{0.125}

Next Step Prepare to Evaluate

∴

V ref = {(\frac{\frac{203.0681}{120} \cdot (0.0028 \cdot 300 + 100) \cdot ({0.28}^{\frac{1 - 0.125}{0.125}})}{5.6553 - 0.0028 \cdot (1200 + \frac{203.0681}{0.28})})}^{0.125}

Next Step Evaluate

∴

V ref = 0.760000252701122m/s

LAST Step Rounding Answer

∴

V ref = 0.76m/s

Reference Cutting Speed given Production Cost per Component 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/s

Note: Value should be greater than 0.

Formulas to find Reference Cutting Velocity

Constant For Machining Condition

Constant For Machining Condition can be regarded as the distance moved by the tool corner relative to the workpiece during a particular machining condition. It is usually measured in Metre.

Symbol: K

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Constant For Machining Condition

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

Machining And Operating Rate

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

Symbol: M

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Machining And Operating Rate

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

Cost of A Tool

The 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

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/s

Note: Value should be greater than 0.

Formulas to find Cutting Velocity

Taylors Tool Life Exponent

Taylors 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 between 0 to 1.

Formulas to find Taylors Tool Life Exponent

Production Cost of Each Component

Production Cost of Each Component is the total amount that it takes to produce a single component from scratch.

Symbol: C_p

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Production Cost of Each Component

Non-Productive Time

Non-Productive Time is the total time wasted in setting up the machine or workpiece for a particular process.

Symbol: NPT

Measurement: TimeUnit: min

Note: Value should be greater than 0.

Formulas to find Non-Productive Time

Other formulas in Production Cost per Component category

Go Production Cost per Component for Constant-Speed-Rough-Machining given Tool Changing Cost

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

Go Production Cost per Component in Constant-Cutting-Speed, Rough-Machining Operation

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

How to Evaluate Reference Cutting Speed given Production Cost per Component?

Reference Cutting Speed given Production Cost per Component evaluator uses Reference Cutting Velocity = ((Constant For Machining Condition/Reference Tool Life*(Machining And Operating Rate*Time to Change One Tool+Cost of A Tool)*(Cutting Velocity^((1-Taylors Tool Life Exponent)/Taylors Tool Life Exponent)))/(Production Cost of Each Component-Machining And Operating Rate*(Non-Productive Time+Constant For Machining Condition/Cutting Velocity)))^Taylors Tool Life Exponent to evaluate the Reference Cutting Velocity, The Reference Cutting Speed given Production Cost per Component is a method to determine the optimal Cutting Velocity required for a given Tool Life in a reference machining condition to manufacture a single component. Reference Cutting Velocity is denoted by V_ref symbol.

How to evaluate Reference Cutting Speed given Production Cost per Component using this online evaluator? To use this online evaluator for Reference Cutting Speed given Production Cost per Component, enter Constant For Machining Condition (K), Reference Tool Life (L_ref), Machining And Operating Rate (M), Time to Change One Tool (t_c), Cost of A Tool (C_t), Cutting Velocity (V), Taylors Tool Life Exponent (n), Production Cost of Each Component (C_p) & Non-Productive Time (NPT) and hit the calculate button.

FAQs on Reference Cutting Speed given Production Cost per Component

What is the formula to find Reference Cutting Speed given Production Cost per Component?

The formula of Reference Cutting Speed given Production Cost per Component is expressed as Reference Cutting Velocity = ((Constant For Machining Condition/Reference Tool Life*(Machining And Operating Rate*Time to Change One Tool+Cost of A Tool)*(Cutting Velocity^((1-Taylors Tool Life Exponent)/Taylors Tool Life Exponent)))/(Production Cost of Each Component-Machining And Operating Rate*(Non-Productive Time+Constant For Machining Condition/Cutting Velocity)))^Taylors Tool Life Exponent. Here is an example- 0.76 = ((203.0681/120*(0.00283*300+100)*(0.28^((1-0.125)/0.125)))/(5.655323-0.00283*(1200+203.0681/0.28)))^0.125.

How to calculate Reference Cutting Speed given Production Cost per Component?

With Constant For Machining Condition (K), Reference Tool Life (L_ref), Machining And Operating Rate (M), Time to Change One Tool (t_c), Cost of A Tool (C_t), Cutting Velocity (V), Taylors Tool Life Exponent (n), Production Cost of Each Component (C_p) & Non-Productive Time (NPT) we can find Reference Cutting Speed given Production Cost per Component using the formula - Reference Cutting Velocity = ((Constant For Machining Condition/Reference Tool Life*(Machining And Operating Rate*Time to Change One Tool+Cost of A Tool)*(Cutting Velocity^((1-Taylors Tool Life Exponent)/Taylors Tool Life Exponent)))/(Production Cost of Each Component-Machining And Operating Rate*(Non-Productive Time+Constant For Machining Condition/Cutting Velocity)))^Taylors Tool Life Exponent.

Can the Reference Cutting Speed given Production Cost per Component be negative?

No, the Reference Cutting Speed given Production Cost per Component, measured in Speed cannot be negative.

Which unit is used to measure Reference Cutting Speed given Production Cost per Component?

Reference Cutting Speed given Production Cost per Component is usually measured using the Meter per Second[m/s] for Speed. Meter per Minute[m/s], Meter per Hour[m/s], Kilometer per Hour[m/s] are the few other units in which Reference Cutting Speed given Production Cost per Component can be measured.

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Reference Cutting Speed given Production Cost per Component Formula

Reference Cutting Speed given Production Cost per Component Example

Reference Cutting Speed given Production Cost per Component Solution

Reference Cutting Speed given Production Cost per Component Formula Elements

Other formulas in Production Cost per Component category

How to Evaluate Reference Cutting Speed given Production Cost per Component?

FAQs on Reference Cutting Speed given Production Cost per Component

Variable Name