Taylor's Exponent given Cutting Speed for Constant-Cutting-Speed Operation 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%
✖Maximum Tool Life is the Tool Life of the tool obtained in the reference Machining Condition.ⓘ Maximum Tool Life [T_max]			+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%
✖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.ⓘ Time Proportion of Cutting Edge Engagement [Q]			+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 Speed for Constant-Cutting-Speed Operation [n]

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Formula

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

Formula

`"n" = ln("V"/"V"_{"ref"})/ln("T"_{"max"}/("T"*"Q"))`

Example

`"0.060606"=ln("8000mm/min"/"5000mm/min")/ln("7000min"/("75min"*"0.04"))`

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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/V_ref)/ln(T_max/(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: 0.04 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

n = ln(V/V_ref)/ln(T_max/(T*Q)) --> ln(0.133333333333333/0.0833333333333333)/ln(420000/(4500*0.04))

Evaluating ... ...

n = 0.0606061133043319

STEP 3: Convert Result to Output's Unit

0.0606061133043319 --> No Conversion Required

FINAL ANSWER

0.0606061133043319 ≈ 0.060606 <-- Taylor's Tool Life Exponent

(Calculation completed in 00.004 seconds)

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

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< 21 Cutting Speed Calculators

Reference Tool Life given Optimum Spindle Speed

Go Reference Tool Life = (((Rotational Frequency of Spindle*2*pi*Outer Radius of Workpiece/Reference Cutting Velocity)^(1/Taylor's Tool Life Exponent))*((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)))))/((1+Taylor's Tool Life Exponent)*Cost of a Tool*(1-Workpiece Radius Ratio))

Optimum Spindle Speed

Go Rotational Frequency of Spindle = (Reference Cutting Velocity/(2*pi*Outer Radius of 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)

Reference Cutting Velocity given Optimum Spindle Speed

Go Reference Cutting Velocity = Rotational Frequency of Spindle*2*pi*Outer Radius of 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*Outer Radius of 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*Outer Radius of 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)

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

Optimum Spindle Speed given Tool Changing Cost

Go Rotational Frequency of Spindle = (Reference Cutting Velocity/(2*pi*Outer Radius of 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 Cost given Optimum Spindle Speed

Go Cost of Changing Each Tool = (Cost of a Tool*Maximum 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

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 = (Outer Radius of Workpiece-(Cutting Velocity/(2*pi*Rotational Frequency of Spindle)))/(Rotational Frequency of Spindle*Feed)

Feed given Instantaneous Cutting Speed

Go Feed = (Outer Radius of Workpiece-(Cutting Velocity/(2*pi*Rotational Frequency of Spindle)))/(Rotational Frequency of Spindle*Process Time)

Instantaneous Cutting Speed given Feed

Go Cutting Velocity = 2*pi*Rotational Frequency of Spindle*(Outer Radius of Workpiece-Rotational Frequency of Spindle*Feed*Process Time)

Reference Cutting Velocity given Rate of Increase of Wear-Land Width

Go Reference Cutting Velocity = Cutting Velocity/((Rate of Increase of Wear Land Width*Reference Tool Life/Maximum Wear Land Width)^Taylor's Tool Life Exponent)

Cutting Velocity given Rate of Increase of Wear-Land Width

Go Cutting Velocity = Reference Cutting Velocity*(Rate of Increase of Wear Land Width*Reference Tool Life/Maximum Wear Land Width)^Taylor's Tool Life Exponent

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

Reference Tool Life given Cutting Speed for Constant-Cutting-Speed Operation

Go Reference Tool Life = ((Cutting Velocity/Reference Cutting Velocity)^(1/Taylor's Tool Life Exponent))*Time Proportion of Cutting Edge Engagement*Tool Life

Tool Life given Cutting Speed for Constant-Cutting-Speed Operation

Go Tool Life = Reference Tool Life*((Reference Cutting Velocity/Cutting Velocity)^(1/Taylor's Tool Life Exponent))/Time Proportion of Cutting Edge Engagement

Reference Cutting Speed given Cutting Speed for Constant-Cutting-Speed Operation

Go Reference Cutting Velocity = Cutting Velocity/((Reference Tool Life/(Tool Life*Time Proportion of Cutting Edge Engagement))^Taylor's Tool Life Exponent)

Cutting Speed for Constant-Cutting-Speed Operation

Go Cutting Velocity = (Reference Tool Life/(Tool Life*Time Proportion of Cutting Edge Engagement))^Taylor's Tool Life Exponent*Reference Cutting Velocity

Rotational Frequency of Spindle given Cutting Speed

Go Rotational Frequency of Spindle = Cutting Velocity/(2*pi*Instantaneous Radius for Cut)

Instantaneous Cutting Speed

Go Cutting Velocity = 2*pi*Rotational Frequency of Spindle*Instantaneous Radius for Cut

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/V_ref)/ln(T_max/(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 (V_ref), Maximum Tool Life (T_max), 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 -> 0.057595 = ln(0.133333333333333/0.0833333333333333)/ln(420000/(4500*0.04)).

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/V_ref)/ln(T_max/(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 (V_ref), Maximum Tool Life (T_max), 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.

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