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

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✖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

`"1.726723"=(-1)*ln("10m/s"/"5m/min")/ln("75min"/"1200min")`

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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 - Natural logarithm function (base e), 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: 10 Meter per Second --> 10 Meter per Second No Conversion Required
Reference Cutting Velocity: 5 Meter per Minute --> 0.0833333333333333 Meter per Second (Check conversion here)
Tool Life: 75 Minute --> 4500 Second (Check conversion here)
Reference Tool Life: 1200 Minute --> 72000 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(10/0.0833333333333333)/ln(4500/72000)

Evaluating ... ...

n = 1.72672264890213

STEP 3: Convert Result to Output's Unit

1.72672264890213 --> No Conversion Required

FINAL ANSWER

1.72672264890213 ≈ 1.726723 <-- Taylor's Tool Life Exponent

(Calculation completed in 00.003 seconds)

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Home » Physics » Metal Machining » Tool Life and Tool Wear » Taylor's Exponent given Cutting Velocities, Tool Lives for two Machining Conditions

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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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< 11 Tool Life and Tool Wear Calculators

Tool temperature

Go Tool Temperature = (Constant for tool temperature*Specific Cutting Energy per unit Cutting Force*Cutting Velocity^0.44*Area of cut^0.22)/(Thermal Conductivity^0.44*Specific Heat Capacity of work^0.56)

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)

Tool Life given Cutting Velocities and Tool Life for Reference Machining Condition

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

Reference Tool Life given Cutting Velocities, Tool Life under Machining Condition

Go Reference Tool Life = Tool Life/((Reference Cutting Velocity/Cutting Velocity)^(1/Taylor's Tool Life Exponent))

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

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

Taylor's Exponent if ratios of Cutting Velocities, Tool Lives are given in two machining conditions

Go Taylor's Tool Life Exponent = (-1)*ln(Ratio of Cutting Velocities)/ln(Ratio of Tool Lives)

Taylor's Tool Life given Cutting Velocity and Intercept

Go Tool Life = (Taylor's Intercept or Taylor's Constant/Cutting Velocity)^(1/Taylor's Tool Life Exponent)

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

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

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 -> 1.726723 = (-1)*ln(10/0.0833333333333333)/ln(4500/72000).

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.

How many ways are there to calculate Taylor's Tool Life Exponent?

In this formula, Taylor's Tool Life Exponent uses Cutting Velocity, Reference Cutting Velocity, Tool Life & Reference Tool Life. We can use 2 other way(s) to calculate the same, which is/are as follows -

Taylor's Tool Life Exponent = ln(Taylor's Intercept or Taylor's Constant/Cutting Velocity)/Tool Life
Taylor's Tool Life Exponent = (-1)*ln(Ratio of Cutting Velocities)/ln(Ratio of Tool Lives)

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