Cutting Velocity for Minimum Production Cost given Tool Changing Cost Calculator

✖Reference Cutting Velocity is the Cutting Velocity of the tool used in the reference Machining Condition.ⓘ Reference Cutting Velocity [V_ref]			+10% -10%
✖Taylor's Tool Life Exponent is an experimental exponent that helps in quantifying the rate of Tool Wear.ⓘ Taylor's Tool Life Exponent [n]			+10% -10%
✖The Cost of a Tool is simply the cost of one tool being used for machining.ⓘ Cost of a Tool [C_t]			+10% -10%
✖Reference Tool Life is the Tool Life of the tool obtained in the reference Machining Condition.ⓘ Reference Tool Life [T_ref]			+10% -10%
✖The cost of changing each Tool is the cost that arises due to the time taken by the operator to change one tool when he is paid by the hour.ⓘ Cost of changing each Tool [C_CT]			+10% -10%

✖The Cutting Velocity is the tangential velocity at the periphery of the cutter or workpiece (whichever is rotating).ⓘ Cutting Velocity for Minimum Production Cost given Tool Changing Cost [V]

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Cutting Velocity for Minimum Production Cost given Tool Changing Cost

Formula

`"V" = "V"_{"ref"}*((("n"*"C"_{"t"}*"T"_{"ref"})/((1-"n")*("C"_{"CT"}+"C"_{"t"})))^"n")`

Example

`"137.083m/s"="5m/min"*((("0.55"*"100"*"12000min")/((1-"0.55")*("25"+"100")))^"0.55")`

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Cutting Velocity for Minimum Production Cost given Tool Changing Cost Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)
V = V_ref*(((n*C_t*T_ref)/((1-n)*(C_CT+C_t)))^n)
This formula uses 6 Variables

Variables Used

Cutting Velocity - (Measured in Meter per Second) - The Cutting Velocity is the tangential velocity at the periphery of the cutter or workpiece (whichever is rotating).
Reference Cutting Velocity - (Measured in Meter per Second) - Reference Cutting Velocity is the Cutting Velocity of the tool used in the reference Machining Condition.
Taylor's Tool Life Exponent - Taylor's Tool Life Exponent is an experimental exponent that helps in quantifying the rate of Tool Wear.
Cost of a Tool - The Cost of a Tool is simply the cost of one tool being used for machining.
Reference Tool Life - (Measured in Second) - Reference Tool Life is the Tool Life of the tool obtained in the reference Machining Condition.
Cost of changing each Tool - The cost of changing each Tool is the cost that arises due to the time taken by the operator to change one tool when he is paid by the hour.

STEP 1: Convert Input(s) to Base Unit

Reference Cutting Velocity: 5 Meter per Minute --> 0.0833333333333333 Meter per Second (Check conversion here)
Taylor's Tool Life Exponent: 0.55 --> No Conversion Required
Cost of a Tool: 100 --> No Conversion Required
Reference Tool Life: 12000 Minute --> 720000 Second (Check conversion here)
Cost of changing each Tool: 25 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

V = V_ref*(((n*C_t*T_ref)/((1-n)*(C_CT+C_t)))^n) --> 0.0833333333333333*(((0.55*100*720000)/((1-0.55)*(25+100)))^0.55)

Evaluating ... ...

V = 137.083036702816

STEP 3: Convert Result to Output's Unit

137.083036702816 Meter per Second --> No Conversion Required

FINAL ANSWER

137.083036702816 ≈ 137.083 Meter per Second <-- Cutting Velocity

(Calculation completed in 00.004 seconds)

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Created by Kumar Siddhant

Indian Institute of Information Technology, Design and Manufacturing (IIITDM), Jabalpur

Kumar Siddhant has created this Calculator and 400+ more calculators!

Verified by Parul Keshav

National Institute of Technology (NIT), Srinagar

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< 20 Minimum Production Cost Calculators

Machining and Operating Rate given Tool Changing Cost

Go Machining and Operating Rate = ((Cost of a Tool+Cost of changing each Tool)/((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))

Machining and Operating Rate using Minimum Production Cost

Go Machining and Operating Rate = (Cost of a Tool/((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 One Tool given Cutting Velocity

Go 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)

Tool Changing Time for each Tool given Cutting Velocity

Go Time to Change One Tool = ((Cost of a Tool*Reference Tool Life/(((Cutting Velocity/Reference Cutting Velocity)^(1/Taylor's Tool Life Exponent))*(1-Taylor's Tool Life Exponent)/Taylor's Tool Life Exponent))-Cost of a Tool)/Cost of a Tool

Reference Tool Life given Cutting Velocity

Go Reference Tool Life = ((Cutting Velocity/Reference Cutting Velocity)^(1/Taylor's Tool Life Exponent))*(1-Taylor's Tool Life Exponent)*(Cost of a Tool*Time to Change One Tool+Cost of a Tool)/(Taylor's Tool Life Exponent*Cost of a Tool)

Reference Cutting Velocity given Cutting Velocity

Go 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)

Cutting Velocity for Minimum Production Cost

Go 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)

Cost of One Tool for Minimum Production Cost given cutting speed

Go 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 to change One Tool given Cutting Velocity

Go Cost of changing each Tool = ((Cost of a Tool*Reference Tool Life/(((Cutting Velocity/Reference Cutting Velocity)^(1/Taylor's Tool Life Exponent))*(1-Taylor's Tool Life Exponent)/Taylor's Tool Life Exponent))-Cost of a Tool)

Cutting Velocity for Minimum Production Cost given Tool Changing Cost

Go 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)

Machining and Operating Rate if cost of changing tool is also considered

Go Machining Rate For Cost Changing Tool = ((Cost of a Tool+Cost of changing each Tool)/Time to Change One Tool)*((1-Taylor's Tool Life Exponent)/(2*Taylor's Tool Life Exponent-1))

Tool Life for Minimum Production Cost

Go Tool Life For Minimum Production Cost = (1-Taylor's Tool Life Exponent)*(Time to Change One Tool+(Cost of a Tool/Cost of a Tool))/Taylor's Tool Life Exponent

Tool Life for Minimum Production Cost given Tool Changing Cost

Go Tool Life = (1-Taylor's Tool Life Exponent)*(Cost of changing each Tool+Cost of a Tool)/(Taylor's Tool Life Exponent*Cost of a Tool)

Tool Changing Time for each Tool given Tool Life and tool cost

Go Time to Change Each Tool = (Tool Life*Taylor's Tool Life Exponent/(1-Taylor's Tool Life Exponent))-(Cost of a Tool/Cost of a Tool)

Cost to change One Tool given Tool Life

Go Cost of changing each Tool = Cost of a Tool*(Tool Life*Taylor's Tool Life Exponent/(1-Taylor's Tool Life Exponent))-Cost of a Tool

Machining and Operating Rate using Min Production Cost and Min Production time

Go Machining and Operating Rate = (Cost of a Tool/Time to Change One Tool)*((1-Taylor's Tool Life Exponent)/(2*Taylor's Tool Life Exponent-1))

Cost of One Tool for Minimum Production Cost given Tool Changing Cost

Go 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 One Tool given Tool Life

Go 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))

Tool Life for Minimum Production Cost when High-Speed Steel Tool is used

Go Tool Life For High Speed Steel = 7*(Time to Change One Tool+(Cost of a Tool/Cost of a Tool))

Tool Life for Minimum Production Cost when Carbide Tool is used

Go Tool Life For Carbide Tool = 3*(Time to Change One Tool+(Cost of a Tool/Cost of a Tool))

Cutting Velocity for Minimum Production Cost given Tool Changing Cost Formula

Ideal Capacity of a Machine Tool

The desired characteristics of a Machine Toole are:
1. Powerful and high Strength
2. Rigid and Stable
3. Tools allows much higher Cutting Velocity, if required and permissible
4. Low wear

How to Calculate Cutting Velocity for Minimum Production Cost given Tool Changing Cost?

Cutting Velocity for Minimum Production Cost given Tool Changing Cost calculator 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 changing each Tool+Cost of a Tool)))^Taylor's Tool Life Exponent) to calculate the Cutting Velocity, The Cutting Velocity for Minimum Production Cost given Tool Changing 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 calculate Cutting Velocity for Minimum Production Cost given Tool Changing Cost using this online calculator? To use this online calculator for Cutting Velocity for Minimum Production Cost given Tool Changing Cost, enter Reference Cutting Velocity (V_ref), Taylor's Tool Life Exponent (n), Cost of a Tool (C_t), Reference Tool Life (T_ref) & Cost of changing each Tool (C_CT) and hit the calculate button. Here is how the Cutting Velocity for Minimum Production Cost given Tool Changing Cost calculation can be explained with given input values -> 137.083 = 0.0833333333333333*(((0.55*100*720000)/((1-0.55)*(25+100)))^0.55).

FAQ

What is Cutting Velocity for Minimum Production Cost given Tool Changing Cost?

The Cutting Velocity for Minimum Production Cost given Tool Changing 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 and is represented as V = V_ref*(((n*C_t*T_ref)/((1-n)*(C_CT+C_t)))^n) or 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). Reference Cutting Velocity is the Cutting Velocity of the tool used in the reference Machining Condition, Taylor's Tool Life Exponent is an experimental exponent that helps in quantifying the rate of Tool Wear, The Cost of a Tool is simply the cost of one tool being used for machining, Reference Tool Life is the Tool Life of the tool obtained in the reference Machining Condition & The cost of changing each Tool is the cost that arises due to the time taken by the operator to change one tool when he is paid by the hour.

How to calculate Cutting Velocity for Minimum Production Cost given Tool Changing Cost?

The Cutting Velocity for Minimum Production Cost given Tool Changing 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 is calculated using 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). To calculate Cutting Velocity for Minimum Production Cost given Tool Changing Cost, you need Reference Cutting Velocity (V_ref), Taylor's Tool Life Exponent (n), Cost of a Tool (C_t), Reference Tool Life (T_ref) & Cost of changing each Tool (C_CT). With our tool, you need to enter the respective value for Reference Cutting Velocity, Taylor's Tool Life Exponent, Cost of a Tool, Reference Tool Life & Cost of changing each Tool and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Cutting Velocity?

In this formula, Cutting Velocity uses Reference Cutting Velocity, Taylor's Tool Life Exponent, Cost of a Tool, Reference Tool Life & Cost of changing each Tool. We can use 1 other way(s) to calculate the same, which is/are as follows -

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)

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