Time Proportion of Cutting Edge Engagement given Tool Life for Minimum Machining Cost Solution

STEP 0: Pre-Calculation Summary
Formula Used
Time Proportion of Cutting Edge Engagement = Tool Life*Taylor's Tool Life Exponent/((1-Taylor's Tool Life Exponent)*(Time to Change One Tool+(Cost of a Tool/Machining and Operating Rate)))
Q = T*n/((1-n)*(tc+(Ct/M)))
This formula uses 6 Variables
Variables Used
Time Proportion of Cutting Edge Engagement - Time Proportion of Cutting Edge Engagement is the fractional portion of machining time during which the Cutting Edge of the tool is engaged with the workpiece.
Tool Life - (Measured in Second) - Tool Life is the period of time for which the cutting edge, affected by the cutting procedure, retains its cutting capacity between sharpening operations.
Taylor's Tool Life Exponent - Taylor's Tool Life Exponent is an experimental exponent that helps in quantifying the rate of Tool Wear.
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.
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.
STEP 1: Convert Input(s) to Base Unit
Tool Life: 75 Minute --> 4500 Second (Check conversion here)
Taylor's Tool Life Exponent: 0.032362 --> No Conversion Required
Time to Change One Tool: 1.25 Minute --> 75 Second (Check conversion here)
Cost of a Tool: 100 --> No Conversion Required
Machining and Operating Rate: 101 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Q = T*n/((1-n)*(tc+(Ct/M))) --> 4500*0.032362/((1-0.032362)*(75+(100/101)))
Evaluating ... ...
Q = 1.98051411438201
STEP 3: Convert Result to Output's Unit
1.98051411438201 --> No Conversion Required
FINAL ANSWER
1.98051411438201 1.980514 <-- Time Proportion of Cutting Edge Engagement
(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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24 Tool and Machining Costs Calculators

Taylor's Exponent for Minimum Machining Cost given Tool Life
Go Taylor's Tool Life Exponent = ((Time to Change One Tool+(Cost of a Tool/Machining and Operating Rate))*Time Proportion of Cutting Edge Engagement)/(Tool Life+((Time to Change One Tool+(Cost of a Tool/Machining and Operating Rate))*Time Proportion of Cutting Edge Engagement))
Machining and Operating Rate given Machining Cost
Go Machining and Operating Rate = ((Machining and Operating Cost of Each Product/Machining Time)-(Time Proportion of Cutting Edge Engagement*Cost of a Tool/Tool Life))/((Time Proportion of Cutting Edge Engagement*Time to Change One Tool/Tool Life)+1)
Tool Changing Time for 1 Tool given Machining Cost
Go Time to Change One Tool = ((Tool Life*((Machining and Operating Cost of Each Product/Machining Time)-Machining and Operating Rate)/Time Proportion of Cutting Edge Engagement)-Cost of a Tool)/Machining and Operating Rate
Tool Life of One Tool given Machining Cost
Go Tool Life = Time Proportion of Cutting Edge Engagement*(Machining and Operating Rate*Time to Change One Tool+Cost of a Tool)/((Machining and Operating Cost of Each Product/Machining Time)-Machining and Operating Rate)
Cost of 1 Tool given Machining Cost
Go Cost of a Tool = (Tool Life*((Machining and Operating Cost of Each Product/Machining Time)-Machining and Operating Rate)/Time Proportion of Cutting Edge Engagement)-(Machining and Operating Rate*Time to Change One Tool)
Time Proportion of Cutting Edge Engagement given Machining Cost
Go Time Proportion of Cutting Edge Engagement = Tool Life*((Machining and Operating Cost of Each Product/Machining Time)-Machining and Operating Rate)/(Machining and Operating Rate*Time to Change One Tool+Cost of a Tool)
Machining Time per component given Machining Cost
Go Machining Time = Machining and Operating Cost of Each Product/(Machining and Operating Rate+(Time Proportion of Cutting Edge Engagement*(Machining and Operating Rate*Time to Change One Tool+Cost of a Tool)/Tool Life))
Machining Cost per component
Go Machining and Operating Cost of Each Product = Machining Time*(Machining and Operating Rate+(Time Proportion of Cutting Edge Engagement*(Machining and Operating Rate*Time to Change One Tool+Cost of a Tool)/Tool Life))
Tool Changing Cost per Tool given Tool Life for Minimum Machining Cost
Go Cost of changing each Tool = (Tool Life*Taylor's Tool Life Exponent*Machining and Operating Rate/(Time Proportion of Cutting Edge Engagement*(1-Taylor's Tool Life Exponent)))-Cost of a Tool
Tool Changing Cost per Tool given Machining Cost
Go Cost of changing each Tool = (Tool Life*((Machining and Operating Cost of Each Product/Machining Time)-Machining and Operating Rate)/Time Proportion of Cutting Edge Engagement)-Cost of a Tool
Machining Cost given Tool Changing Cost per Tool
Go Machining and Operating Cost of Each Product = Machining Time*(Machining and Operating Rate+(Time Proportion of Cutting Edge Engagement*(Cost of changing each Tool+Cost of a Tool)/Tool Life))
Tool Life of One Tool for Minimum Machining Cost given Tool Changing Cost per Tool
Go Tool Life = Time Proportion of Cutting Edge Engagement*(Cost of changing each Tool+Cost of a Tool)*(1-Taylor's Tool Life Exponent)/(Taylor's Tool Life Exponent*Machining and Operating Rate)
Time Proportion of Cutting Edge Engagement given Tool Life for Minimum Machining Cost
Go Time Proportion of Cutting Edge Engagement = Tool Life*Taylor's Tool Life Exponent/((1-Taylor's Tool Life Exponent)*(Time to Change One Tool+(Cost of a Tool/Machining and Operating Rate)))
Tool Changing Time for 1 Tool given Tool Life for Minimum Machining Cost
Go Time to Change One Tool = (Tool Life*Taylor's Tool Life Exponent/((1-Taylor's Tool Life Exponent)*Time Proportion of Cutting Edge Engagement))-(Cost of a Tool/Machining and Operating Rate)
Machining and Operating Rate given Tool Life for Minimum Machining Cost
Go Machining and Operating Rate = Cost of a Tool/((Tool Life*Taylor's Tool Life Exponent/((1-Taylor's Tool Life Exponent)*Time Proportion of Cutting Edge Engagement))-Time to Change One Tool)
Cost of 1 Tool given Tool Life for Minimum Machining Cost
Go Cost of a Tool = ((Tool Life*Taylor's Tool Life Exponent/((1-Taylor's Tool Life Exponent)*Time Proportion of Cutting Edge Engagement))-Time to Change One Tool)*Machining and Operating Rate
Tool Life of One Tool for Minimum Machining Cost
Go Tool Life = Time Proportion of Cutting Edge Engagement*(Time to Change One Tool+(Cost of a Tool/Machining and Operating Rate))*(1-Taylor's Tool Life Exponent)/Taylor's Tool Life Exponent
Taylor's Exponent for Minimum Machining Cost per component
Go Taylor's Tool Life Exponent = 1-(Machining Time for Minimum Cost*Machining and Operating Rate/Machining and Operating Cost of Each Product)
Machining and Operating Rate for Minimum Machining Cost
Go Machining and Operating Rate = Machining and Operating Cost of Each Product*(1-Taylor's Tool Life Exponent)/Machining Time for Minimum Cost
Machining Time per component for Minimum Machining Cost
Go Machining Time for Minimum Cost = Machining and Operating Cost of Each Product*(1-Taylor's Tool Life Exponent)/Machining and Operating Rate
Minimum Cost of Machining per component
Go Machining and Operating Cost of Each Product = Machining and Operating Rate*Machining Time for Minimum Cost/(1-Taylor's Tool Life Exponent)
Cutting Velocity of one product given Constant for Machining Operation
Go Cutting Velocity = Constant For Machining Condition/Machining Time
Constant for Machining Operation of one product given Machining Condition
Go Constant For Machining Condition = Machining Time*Cutting Velocity
Machining Time of one product given Constant for Machining Operation
Go Machining Time = Constant For Machining Condition/Cutting Velocity

Time Proportion of Cutting Edge Engagement given Tool Life for Minimum Machining Cost Formula

Time Proportion of Cutting Edge Engagement = Tool Life*Taylor's Tool Life Exponent/((1-Taylor's Tool Life Exponent)*(Time to Change One Tool+(Cost of a Tool/Machining and Operating Rate)))
Q = T*n/((1-n)*(tc+(Ct/M)))

Advantages of Constant-Cutting-Speed Operation

Constant Surface Speed provides at least four advantages:
1. It simplifies programming.
2. It provides a consistent workpiece finish.
3. It optimizes Tool Life - Tools will always machine at the appropriate speed.
4. It optimizes Machining Time - Cutting conditions will always be properly set, which translates to minimal machining time.

How to Calculate Time Proportion of Cutting Edge Engagement given Tool Life for Minimum Machining Cost?

Time Proportion of Cutting Edge Engagement given Tool Life for Minimum Machining Cost calculator uses Time Proportion of Cutting Edge Engagement = Tool Life*Taylor's Tool Life Exponent/((1-Taylor's Tool Life Exponent)*(Time to Change One Tool+(Cost of a Tool/Machining and Operating Rate))) to calculate the Time Proportion of Cutting Edge Engagement, The Time Proportion of Cutting Edge Engagement given Tool Life for Minimum Machining Cost is a way to determine the time fraction for which the Cutting Edge actually removes material from the workpiece in the given Machining Time. Time Proportion of Cutting Edge Engagement is denoted by Q symbol.

How to calculate Time Proportion of Cutting Edge Engagement given Tool Life for Minimum Machining Cost using this online calculator? To use this online calculator for Time Proportion of Cutting Edge Engagement given Tool Life for Minimum Machining Cost, enter Tool Life (T), Taylor's Tool Life Exponent (n), Time to Change One Tool (tc), Cost of a Tool (Ct) & Machining and Operating Rate (M) and hit the calculate button. Here is how the Time Proportion of Cutting Edge Engagement given Tool Life for Minimum Machining Cost calculation can be explained with given input values -> 0.500015 = 4500*0.032362/((1-0.032362)*(75+(100/101))).

FAQ

What is Time Proportion of Cutting Edge Engagement given Tool Life for Minimum Machining Cost?
The Time Proportion of Cutting Edge Engagement given Tool Life for Minimum Machining Cost is a way to determine the time fraction for which the Cutting Edge actually removes material from the workpiece in the given Machining Time and is represented as Q = T*n/((1-n)*(tc+(Ct/M))) or Time Proportion of Cutting Edge Engagement = Tool Life*Taylor's Tool Life Exponent/((1-Taylor's Tool Life Exponent)*(Time to Change One Tool+(Cost of a Tool/Machining and Operating Rate))). Tool Life is the period of time for which the cutting edge, affected by the cutting procedure, retains its cutting capacity between sharpening operations, Taylor's Tool Life Exponent is an experimental exponent that helps in quantifying the rate of Tool Wear, Time to Change One Tool is the measure of time it takes to change one tool during machining, The Cost of a Tool is simply the cost of one tool being used for machining & Machining and Operating Rate is the money charged for processing on and operating machines per unit time, including overheads.
How to calculate Time Proportion of Cutting Edge Engagement given Tool Life for Minimum Machining Cost?
The Time Proportion of Cutting Edge Engagement given Tool Life for Minimum Machining Cost is a way to determine the time fraction for which the Cutting Edge actually removes material from the workpiece in the given Machining Time is calculated using Time Proportion of Cutting Edge Engagement = Tool Life*Taylor's Tool Life Exponent/((1-Taylor's Tool Life Exponent)*(Time to Change One Tool+(Cost of a Tool/Machining and Operating Rate))). To calculate Time Proportion of Cutting Edge Engagement given Tool Life for Minimum Machining Cost, you need Tool Life (T), Taylor's Tool Life Exponent (n), Time to Change One Tool (tc), Cost of a Tool (Ct) & Machining and Operating Rate (M). With our tool, you need to enter the respective value for Tool Life, Taylor's Tool Life Exponent, Time to Change One Tool, Cost of a Tool & Machining and Operating Rate 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 Time Proportion of Cutting Edge Engagement?
In this formula, Time Proportion of Cutting Edge Engagement uses Tool Life, Taylor's Tool Life Exponent, Time to Change One Tool, Cost of a Tool & Machining and Operating Rate. We can use 1 other way(s) to calculate the same, which is/are as follows -
  • Time Proportion of Cutting Edge Engagement = Tool Life*((Machining and Operating Cost of Each Product/Machining Time)-Machining and Operating Rate)/(Machining and Operating Rate*Time to Change One Tool+Cost of a Tool)
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