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

✖The Cutting Velocity is the tangential velocity at the periphery of the cutter or workpiece (whichever is rotating).ⓘ Cutting Velocity [V]			+10% -10%
✖Reference Cutting Velocity is the Cutting Velocity of the tool used in the reference Machining Condition.ⓘ Reference Cutting Velocity [V_ref]			+10% -10%
✖Tool Life is the period of time for which the cutting edge, affected by the cutting procedure, retains its cutting capacity between sharpening operations.ⓘ Tool Life [T]			+10% -10%
✖Reference Tool Life is the Tool Life of the tool obtained in the reference Machining Condition.ⓘ Reference Tool Life [T_ref]			+10% -10%

✖Taylor's Tool Life Exponent is an experimental exponent that helps in quantifying the rate of Tool Wear.ⓘ Taylor's Exponent given Cutting Velocities, Tool Lives for two Machining Conditions [n]

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Formula

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

Formula

`"n" = (-1)*ln("V"/"V"_{"ref"})/ln("T"/"T"_{"ref"})`

Example

`"0.846625"=(-1)*ln("50m/min"/"1.445m/min")/ln("75min"/"4931.601min")`

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

STEP 0: Pre-Calculation Summary

Formula Used

Taylor's Tool Life Exponent = (-1)*ln(Cutting Velocity/Reference Cutting Velocity)/ln(Tool Life/Reference Tool Life)
n = (-1)*ln(V/V_ref)/ln(T/T_ref)
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

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.
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.
Reference Tool Life - (Measured in Second) - Reference Tool Life is the Tool Life of the tool obtained in the reference Machining Condition.

STEP 1: Convert Input(s) to Base Unit

Cutting Velocity: 50 Meter per Minute --> 0.833333333333333 Meter per Second (Check conversion here)
Reference Cutting Velocity: 1.445 Meter per Minute --> 0.0240833333333333 Meter per Second (Check conversion here)
Tool Life: 75 Minute --> 4500 Second (Check conversion here)
Reference Tool Life: 4931.601 Minute --> 295896.06 Second (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

n = (-1)*ln(V/V_ref)/ln(T/T_ref) --> (-1)*ln(0.833333333333333/0.0240833333333333)/ln(4500/295896.06)

Evaluating ... ...

n = 0.846624995299958

STEP 3: Convert Result to Output's Unit

0.846624995299958 --> No Conversion Required

FINAL ANSWER

0.846624995299958 ≈ 0.846625 <-- Taylor's Tool Life Exponent

(Calculation completed in 00.004 seconds)

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Home » Engineering » Production Engineering » Metal Machining » Machine Tools and Operations » Tool Life and Tool Wear » Cutting Velocity » Taylor's Exponent given Cutting Velocities, Tool Lives for two Machining Conditions

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Indian Institute of Information Technology, Design and Manufacturing (IIITDM), Jabalpur

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< 13 Cutting Velocity Calculators

Cutting Velocity for given Taylor's Tool Life

Go Cutting Velocity = Taylor's Intercept or Taylor's Constant/((Tool Life^Taylor's Tool Life Exponent)*(Feed Rate^Taylor's exponent for Feed Rate)*(Depth of Cut^Taylor's exponent for Depth of Cut))

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

Go Taylor's Tool Life Exponent = (-1)*ln(Cutting Velocity/Reference Cutting Velocity)/ln(Tool Life/Reference Tool Life)

Reference Cutting Velocity given Tool Lives, Cutting Velocity under Machining Condition

Go Reference Cutting Velocity = Cutting Velocity/((Reference Tool Life/Tool Life)^Taylor's Tool Life Exponent)

Cutting Velocity given Tool Lives and Cutting Velocity for Reference Machining Condition

Go Cutting Velocity = Reference Cutting Velocity*(Reference Tool Life/Tool Life)^Taylor's Tool Life Exponent

Cutting Velocity for given Tool Life and Volume of Metal Removed

Go Cutting Velocity = Volume of Metal Removed/(Tool Life*Feed Rate*Depth of Cut)

Taylor's Intercept given Cutting Velocity and Taylor's Tool Life

Go Taylor's Intercept or Taylor's Constant = Taylor Cutting Velocity*(Tool Life^Taylor's Tool Life Exponent)

Cutting Velocity using Taylor's Tool Life and Intercept

Go Taylor Cutting Velocity = Taylor's Intercept or Taylor's Constant/(Tool Life^Taylor's Tool Life Exponent)

Resultant Cutting Velocity

Go Resultant Cutting Velocity = Cutting Velocity/cos((Cutting Speed Angle))

Cutting Speed of Free-Cutting Steel given Cutting Velocity of Tool and Machinability Index

Go Cutting Speed of Free-Cutting Steel = Cutting Velocity*100/Machinability Index of a Material

Cutting Velocity using Machinability Index

Go Cutting Velocity = Machinability Index of a Material*Cutting Speed of Free-Cutting Steel/100

Machinability Index

Go Machinability Index of a Material = Cutting Velocity*100/Cutting Speed of Free-Cutting Steel

Feed for Sintered-Carbide Tools using Crater Depth

Go Feed Rate = (Tool Wear Crater Depth-0.06)/0.3

Crater Depth for Sintered-Carbide Tools

Go Tool Wear Crater Depth = 0.06+0.3*Feed Rate

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

Taylor's Tool Life Exponent = (-1)*ln(Cutting Velocity/Reference Cutting Velocity)/ln(Tool Life/Reference Tool Life)
n = (-1)*ln(V/V_ref)/ln(T/T_ref)

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 Taylor's Tool Life Exponent = (-1)*ln(Cutting Velocity/Reference Cutting Velocity)/ln(Tool Life/Reference Tool Life) to calculate the Taylor's Tool Life Exponent, 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. Taylor's Tool Life Exponent is denoted by n 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 Cutting Velocity (V), Reference Cutting Velocity (V_ref), Tool Life (T) & Reference Tool Life (T_ref) 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 -> 0.846506 = (-1)*ln(0.833333333333333/0.0240833333333333)/ln(4500/295896.06).

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 n = (-1)*ln(V/V_ref)/ln(T/T_ref) or Taylor's Tool Life Exponent = (-1)*ln(Cutting Velocity/Reference Cutting Velocity)/ln(Tool Life/Reference Tool Life). 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, Tool Life 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 is the Tool Life of the tool obtained in the reference 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 Taylor's Tool Life Exponent = (-1)*ln(Cutting Velocity/Reference Cutting Velocity)/ln(Tool Life/Reference Tool Life). To calculate Taylor's Exponent given Cutting Velocities, Tool Lives for two Machining Conditions, you need Cutting Velocity (V), Reference Cutting Velocity (V_ref), Tool Life (T) & Reference Tool Life (T_ref). With our tool, you need to enter the respective value for Cutting Velocity, Reference Cutting Velocity, Tool Life & Reference Tool Life 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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