Time Proportion of Edge given Cutting Speed for Constant-Cutting-Speed Operation Calculator

✖Reference Tool Life refers to a standard or predetermined lifespan used as a baseline for estimating the expected durability of cutting tools under specific machining conditions.ⓘ Reference Tool Life [T_ref]			+10% -10%
✖Reference Cutting Velocity refers to a standard cutting speed used as a baseline or reference point for selecting appropriate cutting speeds for specific machining operations.ⓘ Reference Cutting Velocity [V_ref]			+10% -10%
✖The Cutting Velocity is the tangential velocity at the periphery of the cutter or workpiece (whichever is rotating).ⓘ Cutting Velocity [V]			+10% -10%
✖Taylor's Tool Life Exponent is a parameter used in tool life equations to describe the relationship between cutting speed and tool life in metal machining.ⓘ Taylor's Tool Life Exponent [n]			+10% -10%
✖Tool Life refers to the duration or number of components machined before a cutting tool becomes no longer capable of maintaining the desired machining quality or performance standards.ⓘ Tool Life [T]			+10% -10%

✖Time Proportion of Cutting Edge is the duration during a machining operation that a specific portion of the cutting edge of the tool is actively engaged in removing material from the workpiece.ⓘ Time Proportion of Edge given Cutting Speed for Constant-Cutting-Speed Operation [Q]

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Formula

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Time Proportion of Edge given Cutting Speed for Constant-Cutting-Speed Operation

Formula

`"Q" = "T"_{"ref"}*(("V"_{"ref"}/"V")^(1/"n"))/"T"`

Example

`"0.04"="5min"*(("5000mm/min"/"8000mm/min")^(1/"0.512942"))/"50min"`

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Time Proportion of Edge given Cutting Speed for Constant-Cutting-Speed Operation Solution

STEP 0: Pre-Calculation Summary

Formula Used

Time Proportion of Cutting Edge = Reference Tool Life*((Reference Cutting Velocity/Cutting Velocity)^(1/Taylor's Tool Life Exponent))/Tool Life
Q = T_ref*((V_ref/V)^(1/n))/T
This formula uses 6 Variables

Variables Used

Time Proportion of Cutting Edge - Time Proportion of Cutting Edge is the duration during a machining operation that a specific portion of the cutting edge of the tool is actively engaged in removing material from the workpiece.
Reference Tool Life - (Measured in Second) - Reference Tool Life refers to a standard or predetermined lifespan used as a baseline for estimating the expected durability of cutting tools under specific machining conditions.
Reference Cutting Velocity - (Measured in Meter per Second) - Reference Cutting Velocity refers to a standard cutting speed used as a baseline or reference point for selecting appropriate cutting speeds for specific machining operations.
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).
Taylor's Tool Life Exponent - Taylor's Tool Life Exponent is a parameter used in tool life equations to describe the relationship between cutting speed and tool life in metal machining.
Tool Life - (Measured in Second) - Tool Life refers to the duration or number of components machined before a cutting tool becomes no longer capable of maintaining the desired machining quality or performance standards.

STEP 1: Convert Input(s) to Base Unit

Reference Tool Life: 5 Minute --> 300 Second (Check conversion here)
Reference Cutting Velocity: 5000 Millimeter per Minute --> 0.0833333333333333 Meter per Second (Check conversion here)
Cutting Velocity: 8000 Millimeter per Minute --> 0.133333333333333 Meter per Second (Check conversion here)
Taylor's Tool Life Exponent: 0.512942 --> No Conversion Required
Tool Life: 50 Minute --> 3000 Second (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

Q = T_ref*((V_ref/V)^(1/n))/T --> 300*((0.0833333333333333/0.133333333333333)^(1/0.512942))/3000

Evaluating ... ...

Q = 0.0400000289579246

STEP 3: Convert Result to Output's Unit

0.0400000289579246 --> No Conversion Required

FINAL ANSWER

0.0400000289579246 ≈ 0.04 <-- Time Proportion of Cutting Edge

(Calculation completed in 00.004 seconds)

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Created by Kumar Siddhant

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

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National Institute of Technology (NIT), Srinagar

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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 Spindle Speed)^(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 Spindle Speed/(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 Spindle Speed = Rotational Frequency of Spindle*2*pi*Outer Radius of Workpiece*(((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*Reference Tool Life*(1-Workpiece Radius Ratio)))^Taylor's Tool Life Exponent

Machining and Operating Rate given Optimum Spindle Speed

Go Machining and Operating Rate Spindle Speed = (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)

Tool Changing Time given Optimum Spindle Speed

Go Time to Change One 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)-Cost of a 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 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

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*Maximum 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

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

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

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 given Cutting Speed for Constant-Cutting-Speed Operation

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

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

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

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*Tool Life

Cutting Speed for Constant-Cutting-Speed Operation

Go Cutting Velocity = (Reference Tool Life/(Tool Life*Time Proportion of Cutting Edge))^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

Time Proportion of Edge given Cutting Speed for Constant-Cutting-Speed Operation Formula

Time Proportion of Cutting Edge = Reference Tool Life*((Reference Cutting Velocity/Cutting Velocity)^(1/Taylor's Tool Life Exponent))/Tool Life
Q = T_ref*((V_ref/V)^(1/n))/T

Advantages of Constant-Cutting-Speed Operation

Constant Surface Speed provides at least four advantages:
1. It simplifies programming.
2. It provides a consistent workpiece finish.
3. It optimizes Tool Life - Tools will always machine at the appropriate speed.
4. It optimizes Machining Time - Cutting conditions will always be properly set, which translates to minimal machining time.

How to Calculate Time Proportion of Edge given Cutting Speed for Constant-Cutting-Speed Operation?

Time Proportion of Edge given Cutting Speed for Constant-Cutting-Speed Operation calculator uses Time Proportion of Cutting Edge = Reference Tool Life*((Reference Cutting Velocity/Cutting Velocity)^(1/Taylor's Tool Life Exponent))/Tool Life to calculate the Time Proportion of Cutting Edge, The Time Proportion of Edge given Cutting Speed for Constant-Cutting-Speed Operation refers to the fraction of time during a machining operation that the cutting edge of the tool is actively engaged in cutting the workpiece material. This parameter is influenced by the cutting speed, feed rate, depth of cut, tool geometry, and machining conditions. Time Proportion of Cutting Edge is denoted by Q symbol.

How to calculate Time Proportion of Edge given Cutting Speed for Constant-Cutting-Speed Operation using this online calculator? To use this online calculator for Time Proportion of Edge given Cutting Speed for Constant-Cutting-Speed Operation, enter Reference Tool Life (T_ref), Reference Cutting Velocity (V_ref), Cutting Velocity (V), Taylor's Tool Life Exponent (n) & Tool Life (T) and hit the calculate button. Here is how the Time Proportion of Edge given Cutting Speed for Constant-Cutting-Speed Operation calculation can be explained with given input values -> 56.00004 = 300*((0.0833333333333333/0.133333333333333)^(1/0.512942))/3000.

FAQ

What is Time Proportion of Edge given Cutting Speed for Constant-Cutting-Speed Operation?

The Time Proportion of Edge given Cutting Speed for Constant-Cutting-Speed Operation refers to the fraction of time during a machining operation that the cutting edge of the tool is actively engaged in cutting the workpiece material. This parameter is influenced by the cutting speed, feed rate, depth of cut, tool geometry, and machining conditions and is represented as Q = T_ref*((V_ref/V)^(1/n))/T or Time Proportion of Cutting Edge = Reference Tool Life*((Reference Cutting Velocity/Cutting Velocity)^(1/Taylor's Tool Life Exponent))/Tool Life. Reference Tool Life refers to a standard or predetermined lifespan used as a baseline for estimating the expected durability of cutting tools under specific machining conditions, Reference Cutting Velocity refers to a standard cutting speed used as a baseline or reference point for selecting appropriate cutting speeds for specific machining operations, The Cutting Velocity is the tangential velocity at the periphery of the cutter or workpiece (whichever is rotating), Taylor's Tool Life Exponent is a parameter used in tool life equations to describe the relationship between cutting speed and tool life in metal machining & Tool Life refers to the duration or number of components machined before a cutting tool becomes no longer capable of maintaining the desired machining quality or performance standards.

How to calculate Time Proportion of Edge given Cutting Speed for Constant-Cutting-Speed Operation?

The Time Proportion of Edge given Cutting Speed for Constant-Cutting-Speed Operation refers to the fraction of time during a machining operation that the cutting edge of the tool is actively engaged in cutting the workpiece material. This parameter is influenced by the cutting speed, feed rate, depth of cut, tool geometry, and machining conditions is calculated using Time Proportion of Cutting Edge = Reference Tool Life*((Reference Cutting Velocity/Cutting Velocity)^(1/Taylor's Tool Life Exponent))/Tool Life. To calculate Time Proportion of Edge given Cutting Speed for Constant-Cutting-Speed Operation, you need Reference Tool Life (T_ref), Reference Cutting Velocity (V_ref), Cutting Velocity (V), Taylor's Tool Life Exponent (n) & Tool Life (T). With our tool, you need to enter the respective value for Reference Tool Life, Reference Cutting Velocity, Cutting Velocity, Taylor's Tool Life Exponent & 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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