Taylor's Exponent given Cutting Speed for Constant-Cutting-Speed Operation Solution

STEP 0: Pre-Calculation Summary
Formula Used
Taylor's Tool Life Exponent = ln(Cutting Velocity/Reference Cutting Velocity)/ln(Maximum Tool Life/(Tool Life*Time Proportion of Cutting Edge Engagement))
n = ln(V/Vref)/ln(Tmax/(T*Q))
This formula uses 1 Functions, 6 Variables
Functions Used
ln - The natural logarithm, also known as the logarithm to the base e, is the inverse function of the natural exponential function., ln(Number)
Variables Used
Taylor's Tool Life Exponent - Taylor's Tool Life Exponent is an experimental exponent that helps in quantifying the rate of Tool Wear.
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.
Maximum Tool Life - (Measured in Second) - Maximum Tool Life is the Tool Life of the tool obtained in the reference Machining Condition.
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.
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.
STEP 1: Convert Input(s) to Base Unit
Cutting Velocity: 8000 Millimeter per Minute --> 0.133333333333333 Meter per Second (Check conversion here)
Reference Cutting Velocity: 5000 Millimeter per Minute --> 0.0833333333333333 Meter per Second (Check conversion here)
Maximum Tool Life: 7000 Minute --> 420000 Second (Check conversion here)
Tool Life: 75 Minute --> 4500 Second (Check conversion here)
Time Proportion of Cutting Edge Engagement: 0.4 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
n = ln(V/Vref)/ln(Tmax/(T*Q)) --> ln(0.133333333333333/0.0833333333333333)/ln(420000/(4500*0.4))
Evaluating ... ...
n = 0.0862001620638902
STEP 3: Convert Result to Output's Unit
0.0862001620638902 --> No Conversion Required
FINAL ANSWER
0.0862001620638902 0.0862 <-- Taylor's Tool Life Exponent
(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
Parul Keshav has verified this Calculator and 400+ more calculators!

19 Facing Operation Calculators

Optimum Spindle Speed
Go Rotational Frequency of Spindle = (Reference Cutting Velocity/(2*pi*Outside Radius of the Workpiece))*((((1+Taylor's Tool Life Exponent)*Cost of a Tool*Reference Tool Life*(1-Workpiece Radius Ratio))/((1-Taylor's Tool Life Exponent)*(Cost of a Tool*Time to Change One Tool+Cost of a Tool)*(1-(Workpiece Radius Ratio^((1+Taylor's Tool Life Exponent)/Taylor's Tool Life Exponent)))))^Taylor's Tool Life Exponent)
Machining and Operating Rate given Optimum Spindle Speed
Go Machining and Operating Rate = (Cost of a Tool/(((((((Reference Cutting Velocity/(2*pi*Outside Radius of the Workpiece)))/Rotational Frequency of Spindle)^(1/Taylor's Tool Life Exponent))*((((1+Taylor's Tool Life Exponent)/(1-Taylor's Tool Life Exponent)))*((1-Workpiece Radius Ratio)/(1-((Workpiece Radius Ratio)^((Taylor's Tool Life Exponent+1)/Taylor's Tool Life Exponent))))*Reference Tool Life))))-Time to Change One Tool)
Cost of 1 Tool given Optimum Spindle Speed
Go Cost of a Tool = (Machining and Operating Rate*(((((((Reference Cutting Velocity/(2*pi*Outside Radius of the Workpiece)))/Rotational Frequency of Spindle)^(1/Taylor's Tool Life Exponent))*((((1+Taylor's Tool Life Exponent)/(1-Taylor's Tool Life Exponent)))*((1-Workpiece Radius Ratio)/(1-((Workpiece Radius Ratio)^((Taylor's Tool Life Exponent+1)/Taylor's Tool Life Exponent))))*Maximum Tool Life))))-Time to Change One Tool)
Optimum Spindle Speed given Tool Changing Cost
Go Rotational Frequency of Spindle = (Reference Cutting Velocity/(2*pi*Outside Radius of the Workpiece))*((((1+Taylor's Tool Life Exponent)*Cost of a Tool*Reference Tool Life*(1-Workpiece Radius Ratio))/((1-Taylor's Tool Life Exponent)*(Cost of changing each Tool+Cost of a Tool)*(1-(Workpiece Radius Ratio^((1+Taylor's Tool Life Exponent)/Taylor's Tool Life Exponent)))))^Taylor's Tool Life Exponent)
Tool Changing Time given Optimum Spindle Speed
Go Time to Change One Tool = Reference Tool Life/((Rotational Frequency of Spindle*2*pi*Outer Radius of Workpiece/Reference Cutting Velocity)^(1/Taylor's Tool Life Exponent)*(1-Workpiece Radius Ratio^((1+Taylor's Tool Life Exponent)/Taylor's Tool Life Exponent))*(1-Taylor's Tool Life Exponent)/((1+Taylor's Tool Life Exponent)*(1-Workpiece Radius Ratio)))-Cost of a Tool/Machining and Operating Rate
Tool Changing Cost given Optimum Spindle Speed
Go Cost of changing each Tool = (Cost of a Tool*Maximum Tool Life/(((Rotational Frequency of Spindle*2*pi*Outside Radius of the Workpiece/Reference Cutting Velocity)^(1/Taylor's Tool Life Exponent))*(1-(Workpiece Radius Ratio^((1+Taylor's Tool Life Exponent)/Taylor's Tool Life Exponent)))*(1-Taylor's Tool Life Exponent)/((1+Taylor's Tool Life Exponent)*(1-Workpiece Radius Ratio))))-Cost of a Tool
Machining Time given Rate of Increase of Wear-Land Width
Go Machining Time = Tool Life/(Rate of Increase of Wear Land Width*Reference Tool Life*((Reference Cutting Velocity/Cutting Velocity)^(1/Taylor's Tool Life Exponent))/Increase in Wear Land Width per Component)
Taylor's Exponent given Cutting Speed for Constant-Cutting-Speed Operation
Go Taylor's Tool Life Exponent = ln(Cutting Velocity/Reference Cutting Velocity)/ln(Maximum Tool Life/(Tool Life*Time Proportion of Cutting Edge Engagement))
Time for Facing given Instantaneous Cutting Speed
Go Process Time = (Outside Radius of the Workpiece-(Cutting Velocity/(2*pi*Rotational Frequency of Spindle)))/(Rotational Frequency of Spindle*Feed)
Feed given Instantaneous Cutting Speed
Go Feed = (Outside Radius of the Workpiece-(Cutting Velocity/(2*pi*Rotational Frequency of Spindle)))/(Rotational Frequency of Spindle*Process Time)
Time Proportion of Edge Engagement given Cutting Speed for Constant-Cutting-Speed Operation
Go Time Proportion of Cutting Edge Engagement = Reference Tool Life*((Reference Cutting Velocity/Cutting Velocity)^(1/Taylor's Tool Life Exponent))/Tool Life
Feed of Workpiece given Machining Time for Facing
Go Feed = (Outside Radius of the Workpiece-Inner Radius of Workpiece)/(Rotational Frequency of Spindle*Machining Time)
Total Machining Time for single Facing Operation
Go Machining Time = (Outside Radius of the Workpiece-Inner Radius of Workpiece)/(Rotational Frequency of Spindle*Feed)
Feed given Instantaneous Radius for Cut
Go Feed = (Outside Radius of the Workpiece-Instantaneous Radius for Cut)/(Rotational Frequency of Spindle*Process Time)
Time for Facing
Go Process Time = (Outside Radius of the Workpiece-Instantaneous Radius for Cut)/(Rotational Frequency of Spindle*Feed)
Inner Radius of Workpiece given Machining Time for Facing
Go Inner Radius of Workpiece = Outside Radius of the Workpiece-Rotational Frequency of Spindle*Feed*Machining Time
Machining Time given Maximum Wear-Land Width
Go Machining Time = Increase in Wear Land Width per Component*Tool Life/Maximum Wear Land Width
Inside Radius given Workpiece Radius Ratio
Go Inner Radius of Workpiece = Workpiece Radius Ratio*Outside Radius of the Workpiece
Workpiece Radius Ratio
Go Workpiece Radius Ratio = Inner Radius of Workpiece/Outside Radius of the Workpiece

Taylor's Exponent given Cutting Speed for Constant-Cutting-Speed Operation Formula

Taylor's Tool Life Exponent = ln(Cutting Velocity/Reference Cutting Velocity)/ln(Maximum Tool Life/(Tool Life*Time Proportion of Cutting Edge Engagement))
n = ln(V/Vref)/ln(Tmax/(T*Q))

What is Tool Life ?

Tool life is defined as the time period between two successive grinding of tools and two successive replacement of tools. It is a measure of time or a number of products a single tool can keep machining without restoring its sharpness.

How to Calculate Taylor's Exponent given Cutting Speed for Constant-Cutting-Speed Operation?

Taylor's Exponent given Cutting Speed for Constant-Cutting-Speed Operation calculator uses Taylor's Tool Life Exponent = ln(Cutting Velocity/Reference Cutting Velocity)/ln(Maximum Tool Life/(Tool Life*Time Proportion of Cutting Edge Engagement)) to calculate the Taylor's Tool Life Exponent, The Taylor's Exponent given Cutting Speed for Constant-Cutting-Speed Operation is a method to determine the experimental exponent of Tool Life for the Machining Tool when it is used under a Constant Surface Speed Condition. Taylor's Tool Life Exponent is denoted by n symbol.

How to calculate Taylor's Exponent given Cutting Speed for Constant-Cutting-Speed Operation using this online calculator? To use this online calculator for Taylor's Exponent given Cutting Speed for Constant-Cutting-Speed Operation, enter Cutting Velocity (V), Reference Cutting Velocity (Vref), Maximum Tool Life (Tmax), Tool Life (T) & Time Proportion of Cutting Edge Engagement (Q) and hit the calculate button. Here is how the Taylor's Exponent given Cutting Speed for Constant-Cutting-Speed Operation calculation can be explained with given input values -> -0.262314 = ln(0.133333333333333/0.0833333333333333)/ln(420000/(4500*0.4)).

FAQ

What is Taylor's Exponent given Cutting Speed for Constant-Cutting-Speed Operation?
The Taylor's Exponent given Cutting Speed for Constant-Cutting-Speed Operation is a method to determine the experimental exponent of Tool Life for the Machining Tool when it is used under a Constant Surface Speed Condition and is represented as n = ln(V/Vref)/ln(Tmax/(T*Q)) or Taylor's Tool Life Exponent = ln(Cutting Velocity/Reference Cutting Velocity)/ln(Maximum Tool Life/(Tool Life*Time Proportion of Cutting Edge Engagement)). 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, Maximum Tool Life is the Tool Life of the tool obtained in the reference Machining Condition, Tool Life is the period of time for which the cutting edge, affected by the cutting procedure, retains its cutting capacity between sharpening operations & 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.
How to calculate Taylor's Exponent given Cutting Speed for Constant-Cutting-Speed Operation?
The Taylor's Exponent given Cutting Speed for Constant-Cutting-Speed Operation is a method to determine the experimental exponent of Tool Life for the Machining Tool when it is used under a Constant Surface Speed Condition is calculated using Taylor's Tool Life Exponent = ln(Cutting Velocity/Reference Cutting Velocity)/ln(Maximum Tool Life/(Tool Life*Time Proportion of Cutting Edge Engagement)). To calculate Taylor's Exponent given Cutting Speed for Constant-Cutting-Speed Operation, you need Cutting Velocity (V), Reference Cutting Velocity (Vref), Maximum Tool Life (Tmax), Tool Life (T) & Time Proportion of Cutting Edge Engagement (Q). With our tool, you need to enter the respective value for Cutting Velocity, Reference Cutting Velocity, Maximum Tool Life, Tool Life & Time Proportion of Cutting Edge Engagement and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
Let Others Know
Facebook
Twitter
Reddit
LinkedIn
Email
WhatsApp
Copied!