Cutting Velocity for Minimum Production 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 a Tool*Time to Change One Tool+Cost of a Tool)))^Taylor's Tool Life Exponent)
V = Vref*(((n*Ct*Tref)/((1-n)*(Ct*tc+Ct)))^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.
Time to Change One Tool - (Measured in Second) - Time to Change One Tool is the measure of time it takes to change one tool during machining.
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)
Time to Change One Tool: 1.5 Minute --> 90 Second (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
V = Vref*(((n*Ct*Tref)/((1-n)*(Ct*tc+Ct)))^n) --> 0.0833333333333333*(((0.55*100*720000)/((1-0.55)*(100*90+100)))^0.55)
Evaluating ... ...
V = 12.9661624316079
STEP 3: Convert Result to Output's Unit
12.9661624316079 Meter per Second --> No Conversion Required
FINAL ANSWER
12.9661624316079 12.96616 Meter per Second <-- Cutting Velocity
(Calculation completed in 00.004 seconds)

Credits

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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10+ Cutting Velocity for 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)

Cutting Velocity for Minimum Production Cost Formula

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)
V = Vref*(((n*Ct*Tref)/((1-n)*(Ct*tc+Ct)))^n)

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?

Cutting Velocity for Minimum Production 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 a Tool*Time to Change One Tool+Cost of a Tool)))^Taylor's Tool Life Exponent) to calculate the Cutting Velocity, The Cutting Velocity for Minimum Production 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 using this online calculator? To use this online calculator for Cutting Velocity for Minimum Production Cost, enter Reference Cutting Velocity (Vref), Taylor's Tool Life Exponent (n), Cost of a Tool (Ct), Reference Tool Life (Tref) & Time to Change One Tool (tc) and hit the calculate button. Here is how the Cutting Velocity for Minimum Production Cost calculation can be explained with given input values -> 12.96616 = 0.0833333333333333*(((0.55*100*720000)/((1-0.55)*(100*90+100)))^0.55).

FAQ

What is Cutting Velocity for Minimum Production Cost?
The Cutting Velocity for Minimum Production 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 = Vref*(((n*Ct*Tref)/((1-n)*(Ct*tc+Ct)))^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 a Tool*Time to Change One 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 & Time to Change One Tool is the measure of time it takes to change one tool during machining.
How to calculate Cutting Velocity for Minimum Production Cost?
The Cutting Velocity for Minimum Production 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 a Tool*Time to Change One Tool+Cost of a Tool)))^Taylor's Tool Life Exponent). To calculate Cutting Velocity for Minimum Production Cost, you need Reference Cutting Velocity (Vref), Taylor's Tool Life Exponent (n), Cost of a Tool (Ct), Reference Tool Life (Tref) & Time to Change One Tool (tc). 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 & Time to Change One 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 & Time to Change One 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 changing each Tool+Cost of a Tool)))^Taylor's Tool Life Exponent)
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