## Taylor's Exponent given Cutting Velocities, Tool Lives for two Machining Conditions Solution

STEP 0: Pre-Calculation Summary
Formula Used
Taylors Tool Life Exponent in Cutting Velocity = (-1)*ln(Cut Velocity/Reference Cutting Velocity in Cutting Velocity)/ln(Tool Life in Cutting Velocity/Reference Tool Life in Cutting Velocity)
x = (-1)*ln(Vcut/Vrf)/ln(Tv/Trf)
This formula uses 1 Functions, 5 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
Taylors Tool Life Exponent in Cutting Velocity - Taylors Tool Life Exponent in Cutting Velocity is an experimental exponent that helps in quantifying the rate of tool wear.
Cut Velocity - (Measured in Meter per Second) - The Cut Velocity is the tangential velocity at the periphery of the cutter or workpiece (whichever is rotating).
Reference Cutting Velocity in Cutting Velocity - (Measured in Meter per Second) - Reference Cutting Velocity in Cutting Velocity is the cutting velocity of the tool used in the reference to machining condition.
Tool Life in Cutting Velocity - (Measured in Second) - Tool Life in Cutting Velocity is the period of time for which the cutting edge, affected by the cutting procedure, retains its cutting capacity between sharpening operations.
Reference Tool Life in Cutting Velocity - (Measured in Second) - Reference Tool Life in Cutting Velocity is the tool life of the tool obtained in the reference to machining condition.
STEP 1: Convert Input(s) to Base Unit
Cut Velocity: 0.831666667 Meter per Second --> 0.831666667 Meter per Second No Conversion Required
Reference Cutting Velocity in Cutting Velocity: 0.024066667 Meter per Second --> 0.024066667 Meter per Second No Conversion Required
Tool Life in Cutting Velocity: 4499.4 Second --> 4499.4 Second No Conversion Required
Reference Tool Life in Cutting Velocity: 295896.06 Second --> 295896.06 Second No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
x = (-1)*ln(Vcut/Vrf)/ln(Tv/Trf) --> (-1)*ln(0.831666667/0.024066667)/ln(4499.4/295896.06)
Evaluating ... ...
x = 0.846285147218067
STEP 3: Convert Result to Output's Unit
0.846285147218067 --> No Conversion Required
0.846285147218067 0.846285 <-- Taylors Tool Life Exponent in Cutting Velocity
(Calculation completed in 00.004 seconds)
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## 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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## < 13 Cutting Velocity Calculators

Cutting Velocity for given Taylor's Tool Life
Cut Velocity = Taylors Intercept or Taylor's Constant/((Tool Life in Cutting Velocity^Taylors Tool Life Exponent in Cutting Velocity)*(Feed Rate in Cutting Velocity^Taylors Exponent For Feed Rate in Cutting Velocity)*(Cut Depth^Taylor's Exponent in Cutting Velocity))
Taylor's Exponent given Cutting Velocities, Tool Lives for two Machining Conditions
Taylors Tool Life Exponent in Cutting Velocity = (-1)*ln(Cut Velocity/Reference Cutting Velocity in Cutting Velocity)/ln(Tool Life in Cutting Velocity/Reference Tool Life in Cutting Velocity)
Reference Cutting Velocity given Tool Lives, Cutting Velocity under Machining Condition
Reference Cutting Velocity in Cutting Velocity = Cut Velocity/((Reference Tool Life in Cutting Velocity/Tool Life in Cutting Velocity)^Taylors Tool Life Exponent in Cutting Velocity)
Cutting Velocity given Tool Lives and Cutting Velocity for Reference Machining Condition
Cut Velocity = Reference Cutting Velocity in Cutting Velocity*(Reference Tool Life in Cutting Velocity/Tool Life in Cutting Velocity)^Taylors Tool Life Exponent in Cutting Velocity
Taylor's Intercept given Cutting Velocity and Taylor's Tool Life
Taylors Intercept or Taylor's Constant = Taylor Cutting Velocity*(Tool Life in Cutting Velocity^Taylors Tool Life Exponent in Cutting Velocity)
Cutting Velocity using Taylor's Tool Life and Intercept
Taylor Cutting Velocity = Taylors Intercept or Taylor's Constant/(Tool Life in Cutting Velocity^Taylors Tool Life Exponent in Cutting Velocity)
Cutting Velocity for given Tool Life and Volume of Metal Removed
Cut Velocity = Volume of Metal Removed/(Tool Life in Cutting Velocity*Feed Rate in Cutting Velocity*Cut Depth)
Resultant Cutting Velocity
Resultant Cutting Velocity = Cutting Velocity/cos((Cutting Speed Angle))
Cutting Speed of Free-Cutting Steel given Cutting Velocity of Tool and Machinability Index
Cutting Speed of Free-Cutting Steel = Cut Velocity*100/Machinability Index of A Material
Cutting Velocity using Machinability Index
Cut Velocity = Machinability Index of A Material*Cutting Speed of Free-Cutting Steel/100
Machinability Index
Machinability Index of A Material = Cut Velocity*100/Cutting Speed of Free-Cutting Steel
Feed for Sintered-Carbide Tools using Crater Depth
Feed Rate in Cutting Velocity = (Tool Wear Crater Depth-0.06)/0.3
Crater Depth for Sintered-Carbide Tools
Tool Wear Crater Depth = 0.06+0.3*Feed Rate in Cutting Velocity

## Taylor's Exponent given Cutting Velocities, Tool Lives for two Machining Conditions Formula

Taylors Tool Life Exponent in Cutting Velocity = (-1)*ln(Cut Velocity/Reference Cutting Velocity in Cutting Velocity)/ln(Tool Life in Cutting Velocity/Reference Tool Life in Cutting Velocity)
x = (-1)*ln(Vcut/Vrf)/ln(Tv/Trf)

## 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 Taylor's Exponent given Cutting Velocities, Tool Lives for two Machining Conditions?

Taylor's Exponent given Cutting Velocities, Tool Lives for two Machining Conditions calculator uses Taylors Tool Life Exponent in Cutting Velocity = (-1)*ln(Cut Velocity/Reference Cutting Velocity in Cutting Velocity)/ln(Tool Life in Cutting Velocity/Reference Tool Life in Cutting Velocity) to calculate the Taylors Tool Life Exponent in Cutting Velocity, The Taylor's Exponent given Cutting Velocities, Tool Lives for two machining conditions is a method to determine the Taylor's Tool Life Exponent when comparison has been made between two Machining Conditions with the same tool. Taylors Tool Life Exponent in Cutting Velocity is denoted by x symbol.

How to calculate Taylor's Exponent given Cutting Velocities, Tool Lives for two Machining Conditions using this online calculator? To use this online calculator for Taylor's Exponent given Cutting Velocities, Tool Lives for two Machining Conditions, enter Cut Velocity (Vcut), Reference Cutting Velocity in Cutting Velocity (Vrf), Tool Life in Cutting Velocity (Tv) & Reference Tool Life in Cutting Velocity (Trf) and hit the calculate button. Here is how the Taylor's Exponent given Cutting Velocities, Tool Lives for two Machining Conditions calculation can be explained with given input values -> 0.846285 = (-1)*ln(0.831666667/0.024066667)/ln(4499.4/295896.06).

### FAQ

What is Taylor's Exponent given Cutting Velocities, Tool Lives for two Machining Conditions?
The Taylor's Exponent given Cutting Velocities, Tool Lives for two machining conditions is a method to determine the Taylor's Tool Life Exponent when comparison has been made between two Machining Conditions with the same tool and is represented as x = (-1)*ln(Vcut/Vrf)/ln(Tv/Trf) or Taylors Tool Life Exponent in Cutting Velocity = (-1)*ln(Cut Velocity/Reference Cutting Velocity in Cutting Velocity)/ln(Tool Life in Cutting Velocity/Reference Tool Life in Cutting Velocity). The Cut Velocity is the tangential velocity at the periphery of the cutter or workpiece (whichever is rotating), Reference Cutting Velocity in Cutting Velocity is the cutting velocity of the tool used in the reference to machining condition, Tool Life in Cutting Velocity is the period of time for which the cutting edge, affected by the cutting procedure, retains its cutting capacity between sharpening operations & Reference Tool Life in Cutting Velocity is the tool life of the tool obtained in the reference to machining condition.
How to calculate Taylor's Exponent given Cutting Velocities, Tool Lives for two Machining Conditions?
The Taylor's Exponent given Cutting Velocities, Tool Lives for two machining conditions is a method to determine the Taylor's Tool Life Exponent when comparison has been made between two Machining Conditions with the same tool is calculated using Taylors Tool Life Exponent in Cutting Velocity = (-1)*ln(Cut Velocity/Reference Cutting Velocity in Cutting Velocity)/ln(Tool Life in Cutting Velocity/Reference Tool Life in Cutting Velocity). To calculate Taylor's Exponent given Cutting Velocities, Tool Lives for two Machining Conditions, you need Cut Velocity (Vcut), Reference Cutting Velocity in Cutting Velocity (Vrf), Tool Life in Cutting Velocity (Tv) & Reference Tool Life in Cutting Velocity (Trf). With our tool, you need to enter the respective value for Cut Velocity, Reference Cutting Velocity in Cutting Velocity, Tool Life in Cutting Velocity & Reference Tool Life in Cutting Velocity 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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