Reference Tool Life given Cutting Velocity Solution

STEP 0: Pre-Calculation Summary
Formula Used
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)
Tref = ((V/Vref)^(1/n))*(1-n)*(Ct*tc+Ct)/(n*Ct)
This formula uses 6 Variables
Variables Used
Reference Tool Life - (Measured in Second) - Reference Tool Life is the Tool Life of the tool obtained 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).
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.
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
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
Time to Change One Tool: 1.5 Minute --> 90 Second (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Tref = ((V/Vref)^(1/n))*(1-n)*(Ct*tc+Ct)/(n*Ct) --> ((7/0.0833333333333333)^(1/0.55))*(1-0.55)*(100*90+100)/(0.55*100)
Evaluating ... ...
Tref = 234736.609616464
STEP 3: Convert Result to Output's Unit
234736.609616464 Second -->3912.27682694106 Minute (Check conversion here)
FINAL ANSWER
3912.27682694106 3912.277 Minute <-- Reference Tool Life
(Calculation completed in 00.020 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)

Reference Tool Life given Cutting Velocity Formula

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

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 Tool Life given Cutting Velocity?

Reference Tool Life given Cutting Velocity calculator uses 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) to calculate the Reference Tool Life, The Reference Tool Life given Cutting Velocity is a method to determine the optimal Tool Sharpening period required in reference machining condition to manufacture a given batch of components such that The Total Production Cost is minimum. Reference Tool Life is denoted by Tref symbol.

How to calculate Reference Tool Life given Cutting Velocity using this online calculator? To use this online calculator for Reference Tool Life given Cutting Velocity, enter Cutting Velocity (V), Reference Cutting Velocity (Vref), Taylor's Tool Life Exponent (n), Cost of a Tool (Ct) & Time to Change One Tool (tc) and hit the calculate button. Here is how the Reference Tool Life given Cutting Velocity calculation can be explained with given input values -> 65.20461 = ((7/0.0833333333333333)^(1/0.55))*(1-0.55)*(100*90+100)/(0.55*100).

FAQ

What is Reference Tool Life given Cutting Velocity?
The Reference Tool Life given Cutting Velocity is a method to determine the optimal Tool Sharpening period required in reference machining condition to manufacture a given batch of components such that The Total Production Cost is minimum and is represented as Tref = ((V/Vref)^(1/n))*(1-n)*(Ct*tc+Ct)/(n*Ct) or 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). The Cutting Velocity is the tangential velocity at the periphery of the cutter or workpiece (whichever is rotating), 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 & Time to Change One Tool is the measure of time it takes to change one tool during machining.
How to calculate Reference Tool Life given Cutting Velocity?
The Reference Tool Life given Cutting Velocity is a method to determine the optimal Tool Sharpening period required in reference machining condition to manufacture a given batch of components such that The Total Production Cost is minimum is calculated using 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). To calculate Reference Tool Life given Cutting Velocity, you need Cutting Velocity (V), Reference Cutting Velocity (Vref), Taylor's Tool Life Exponent (n), Cost of a Tool (Ct) & Time to Change One Tool (tc). With our tool, you need to enter the respective value for Cutting Velocity, Reference Cutting Velocity, Taylor's Tool Life Exponent, Cost of a Tool & 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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