Reference Cutting Velocity given Cutting Velocity Solution

STEP 0: Pre-Calculation Summary
Formula Used
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)
Vref = V/(((n*Ct*Tref)/((1-n)*(Ct*tc+Ct)))^n)
This formula uses 6 Variables
Variables Used
Reference Cutting Velocity - (Measured in Meter per Second) - Reference Cutting Velocity is the Cutting Velocity of the tool used in the reference Machining Condition.
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).
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
Cutting Velocity: 7 Meter per Second --> 7 Meter per Second No Conversion Required
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
Vref = V/(((n*Ct*Tref)/((1-n)*(Ct*tc+Ct)))^n) --> 7/(((0.55*100*720000)/((1-0.55)*(100*90+100)))^0.55)
Evaluating ... ...
Vref = 0.0449888960137756
STEP 3: Convert Result to Output's Unit
0.0449888960137756 Meter per Second -->2.69933376082654 Meter per Minute (Check conversion here)
FINAL ANSWER
2.69933376082654 2.699334 Meter per Minute <-- Reference Cutting Velocity
(Calculation completed in 00.020 seconds)

Credits

Created by Kumar Siddhant
Indian Institute of Information Technology, Design and Manufacturing (IIITDM), Jabalpur
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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)

Reference Cutting Velocity given Cutting Velocity 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)
Vref = V/(((n*Ct*Tref)/((1-n)*(Ct*tc+Ct)))^n)

What is Reference Machining Condition?

Reference Machining Condition is usually a state of Machining Operation which has been idealized as the most suitable. It is used to draw a comparison between different other Machining Conditions.

How to Calculate Reference Cutting Velocity given Cutting Velocity?

Reference Cutting Velocity given Cutting Velocity calculator 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 calculate 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 Vref symbol.

How to calculate Reference Cutting Velocity given Cutting Velocity using this online calculator? To use this online calculator for Reference Cutting Velocity given Cutting Velocity, enter Cutting Velocity (V), 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 Reference Cutting Velocity given Cutting Velocity calculation can be explained with given input values -> 161.96 = 7/(((0.55*100*720000)/((1-0.55)*(100*90+100)))^0.55).

FAQ

What is Reference Cutting Velocity given 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 and is represented as Vref = V/(((n*Ct*Tref)/((1-n)*(Ct*tc+Ct)))^n) or 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). The Cutting Velocity is the tangential velocity at the periphery of the cutter or workpiece (whichever is rotating), 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 Reference Cutting Velocity given 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 is calculated using 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 calculate Reference Cutting Velocity given Cutting Velocity, you need Cutting Velocity (V), 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 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.
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