Cost of One Tool given Cutting Velocity Solution

STEP 0: Pre-Calculation Summary
Formula Used
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)
Ct = M*((Tref*(nh/(nh-1))*((Vref/V)^(1/nh)))-tc)
This formula uses 7 Variables
Variables Used
Cost of a Tool - The Cost of a Tool is simply the cost of one tool being used for machining.
Machining and Operating Rate - Machining and Operating Rate is the money charged for processing on and operating machines per unit time, including overheads for minimum production cost.
Reference Tool Life - (Measured in Second) - Reference Tool Life is the Tool Life of the tool obtained in the reference Machining Condition.
Taylor's Tool Life Exponent for Hard Material - Taylor's Tool Life Exponent for Hard Material is a parameter used in machining operations to describe the relationship between cutting speed and tool life.
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).
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
Machining and Operating Rate: 0.44 --> No Conversion Required
Reference Tool Life: 12000 Minute --> 720000 Second (Check conversion here)
Taylor's Tool Life Exponent for Hard Material: 1.55 --> No Conversion Required
Reference Cutting Velocity: 5 Meter per Minute --> 0.0833333333333333 Meter per Second (Check conversion here)
Cutting Velocity: 7 Meter per Second --> 7 Meter per Second 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
Ct = M*((Tref*(nh/(nh-1))*((Vref/V)^(1/nh)))-tc) --> 0.44*((720000*(1.55/(1.55-1))*((0.0833333333333333/7)^(1/1.55)))-90)
Evaluating ... ...
Ct = 51162.0167401169
STEP 3: Convert Result to Output's Unit
51162.0167401169 --> No Conversion Required
FINAL ANSWER
51162.0167401169 51162.02 <-- Cost of a Tool
(Calculation completed in 00.019 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)

Cost of One Tool given Cutting Velocity Formula

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)
Ct = M*((Tref*(nh/(nh-1))*((Vref/V)^(1/nh)))-tc)

Significance of Cost of Tools Used

The Cost of Tools Used helps us in determining the maximum number of times a tool can be renewed during the production of a given batch of products. This renewing might include buying or resharpening the tool. Thus if the number of Tools to be used gets bounded, the machining operation would have to be optimized in order to give sufficient tool life to minimize the Total Cost of Production.

How to Calculate Cost of One Tool given Cutting Velocity?

Cost of One Tool given Cutting Velocity calculator uses 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) to calculate the Cost of a Tool, The Cost of One Tool given Cutting Velocity is a method to determine the maximum amount available to be spent on renewing the Machining Tool for the production of a batch of components, such that the Total Production Cost is Minimum. Cost of a Tool is denoted by Ct symbol.

How to calculate Cost of One Tool given Cutting Velocity using this online calculator? To use this online calculator for Cost of One Tool given Cutting Velocity, enter Machining and Operating Rate (M), Reference Tool Life (Tref), Taylor's Tool Life Exponent for Hard Material (nh), Reference Cutting Velocity (Vref), Cutting Velocity (V) & Time to Change One Tool (tc) and hit the calculate button. Here is how the Cost of One Tool given Cutting Velocity calculation can be explained with given input values -> -162.413395 = 0.44*((720000*(1.55/(1.55-1))*((0.0833333333333333/7)^(1/1.55)))-90).

FAQ

What is Cost of One Tool given Cutting Velocity?
The Cost of One Tool given Cutting Velocity is a method to determine the maximum amount available to be spent on renewing the Machining Tool for the production of a batch of components, such that the Total Production Cost is Minimum and is represented as Ct = M*((Tref*(nh/(nh-1))*((Vref/V)^(1/nh)))-tc) or 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). Machining and Operating Rate is the money charged for processing on and operating machines per unit time, including overheads for minimum production cost, Reference Tool Life is the Tool Life of the tool obtained in the reference Machining Condition, Taylor's Tool Life Exponent for Hard Material is a parameter used in machining operations to describe the relationship between cutting speed and tool life, Reference Cutting Velocity is the Cutting Velocity of the tool used in the reference Machining Condition, The Cutting Velocity is the tangential velocity at the periphery of the cutter or workpiece (whichever is rotating) & Time to Change One Tool is the measure of time it takes to change one tool during machining.
How to calculate Cost of One Tool given Cutting Velocity?
The Cost of One Tool given Cutting Velocity is a method to determine the maximum amount available to be spent on renewing the Machining Tool for the production of a batch of components, such that the Total Production Cost is Minimum is calculated using 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). To calculate Cost of One Tool given Cutting Velocity, you need Machining and Operating Rate (M), Reference Tool Life (Tref), Taylor's Tool Life Exponent for Hard Material (nh), Reference Cutting Velocity (Vref), Cutting Velocity (V) & Time to Change One Tool (tc). With our tool, you need to enter the respective value for Machining and Operating Rate, Reference Tool Life, Taylor's Tool Life Exponent for Hard Material, Reference Cutting Velocity, Cutting Velocity & 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 Cost of a Tool?
In this formula, Cost of a Tool uses Machining and Operating Rate, Reference Tool Life, Taylor's Tool Life Exponent for Hard Material, Reference Cutting Velocity, Cutting Velocity & Time to Change One Tool. We can use 1 other way(s) to calculate the same, which is/are as follows -
  • 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)
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