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Reference Tool Life given Optimum Spindle Speed Calculator

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✖Rotational Frequency of Spindle is the number of turns made by the spindle of the Machine for cutting in one second.ⓘ Rotational Frequency of Spindle [ns]
+10%
-10%
✖Outer Radius of Workpiece is the radius of the outermost surface of the workpiece, away from the machining tool.ⓘ Outer Radius of Workpiece [Ro]
+10%
-10%
✖Reference Cutting Velocity is the Cutting Velocity of the tool used in the reference Machining Condition.ⓘ Reference Cutting Velocity [Vref]
+10%
-10%
✖Taylor's Tool Life Exponent is an experimental exponent that helps in quantifying the rate of Tool Wear.ⓘ Taylor's Tool Life Exponent [n]
+10%
-10%
✖The Cost of a Tool is simply the cost of one tool being used for machining.ⓘ Cost of a Tool [Ct]
+10%
-10%
✖Time to Change One Tool is the measure of time it takes to change one tool during machining.ⓘ Time to Change One Tool [tc]
+10%
-10%
✖Workpiece Radius Ratio is the ratio of the inner radius of the workpiece to its outer radius.ⓘ Workpiece Radius Ratio [ar]
+10%
-10%
✖Reference Tool Life is the Tool Life of the tool obtained in the reference Machining Condition.ⓘ Reference Tool Life given Optimum Spindle Speed [Tref]
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Formula
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Reference Tool Life given Optimum Spindle Speed

Formula
`"T"_{"ref"} = ((("n"_{"s"}*2*pi*"R"_{"o"}/"V"_{"ref"})^(1/"n"))*((1-"n")*("C"_{"t"}*"t"_{"c"}+"C"_{"t"})*(1-("a"_{"r"}^((1+"n")/"n")))))/((1+"n")*"C"_{"t"}*(1-"a"_{"r"}))`

Example
`"400.0636min"=((("0.050885Hz"*2*pi*"10000mm"/"5000mm/min")^(1/"0.512942"))*((1-"0.512942")*("70"*"0.6min"+"70")*(1-(("0.45")^((1+"0.512942")/"0.512942")))))/((1+"0.512942")*"70"*(1-"0.45"))`

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Reference Tool Life given Optimum Spindle Speed Solution

STEP 0: Pre-Calculation Summary
Formula Used
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))
Tref = (((ns*2*pi*Ro/Vref)^(1/n))*((1-n)*(Ct*tc+Ct)*(1-(ar^((1+n)/n)))))/((1+n)*Ct*(1-ar))
This formula uses 1 Constants, 8 Variables
Constants Used
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
Variables Used
Reference Tool Life - (Measured in Second) - Reference Tool Life is the Tool Life of the tool obtained in the reference Machining Condition.
Rotational Frequency of Spindle - (Measured in Hertz) - Rotational Frequency of Spindle is the number of turns made by the spindle of the Machine for cutting in one second.
Outer Radius of Workpiece - (Measured in Meter) - Outer Radius of Workpiece is the radius of the outermost surface of the workpiece, away from the machining tool.
Reference Cutting Velocity - (Measured in Meter per Second) - Reference Cutting Velocity is the Cutting Velocity of the tool used in the reference Machining Condition.
Taylor's Tool Life Exponent - Taylor's Tool Life Exponent is an experimental exponent that helps in quantifying the rate of Tool Wear.
Cost of a Tool - The Cost of a Tool is simply the cost of one tool being used for machining.
Time to Change One Tool - (Measured in Second) - Time to Change One Tool is the measure of time it takes to change one tool during machining.
Workpiece Radius Ratio - Workpiece Radius Ratio is the ratio of the inner radius of the workpiece to its outer radius.
STEP 1: Convert Input(s) to Base Unit
Rotational Frequency of Spindle: 0.050885 Hertz --> 0.050885 Hertz No Conversion Required
Outer Radius of Workpiece: 10000 Millimeter --> 10 Meter (Check conversion ​here)
Reference Cutting Velocity: 5000 Millimeter per Minute --> 0.0833333333333333 Meter per Second (Check conversion ​here)
Taylor's Tool Life Exponent: 0.512942 --> No Conversion Required
Cost of a Tool: 70 --> No Conversion Required
Time to Change One Tool: 0.6 Minute --> 36 Second (Check conversion ​here)
Workpiece Radius Ratio: 0.45 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Tref = (((ns*2*pi*Ro/Vref)^(1/n))*((1-n)*(Ct*tc+Ct)*(1-(ar^((1+n)/n)))))/((1+n)*Ct*(1-ar)) --> (((0.050885*2*pi*10/0.0833333333333333)^(1/0.512942))*((1-0.512942)*(70*36+70)*(1-(0.45^((1+0.512942)/0.512942)))))/((1+0.512942)*70*(1-0.45))
Evaluating ... ...
Tref = 24003.8132880955
STEP 3: Convert Result to Output's Unit
24003.8132880955 Second -->400.063554801592 Minute (Check conversion ​here)
FINAL ANSWER
400.063554801592 ≈ 400.0636 Minute <-- Reference Tool Life
(Calculation completed in 00.004 seconds)
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Created by Kumar Siddhant
Indian Institute of Information Technology, Design and Manufacturing (IIITDM), Jabalpur
Kumar Siddhant has created this Calculator and 400+ more calculators!
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Verified by Parul Keshav
National Institute of Technology (NIT), Srinagar
Parul Keshav has verified this Calculator and 400+ more calculators!

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

Reference Tool Life given Optimum Spindle Speed Formula

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))
Tref = (((ns*2*pi*Ro/Vref)^(1/n))*((1-n)*(Ct*tc+Ct)*(1-(ar^((1+n)/n)))))/((1+n)*Ct*(1-ar))

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 Reference Tool Life given Optimum Spindle Speed?

Reference Tool Life given Optimum Spindle Speed calculator uses 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)) to calculate the Reference Tool Life, The Reference Tool Life given Optimum Spindle Speed is a method to determine the tool Life of a Machining Tool when used under the reference condition such that the Facing Operation finishes at minimum expense. Reference Tool Life is denoted by Tref symbol.

How to calculate Reference Tool Life given Optimum Spindle Speed using this online calculator? To use this online calculator for Reference Tool Life given Optimum Spindle Speed, enter Rotational Frequency of Spindle (ns), Outer Radius of Workpiece (Ro), Reference Cutting Velocity (Vref), Taylor's Tool Life Exponent (n), Cost of a Tool (Ct), Time to Change One Tool (tc) & Workpiece Radius Ratio (ar) and hit the calculate button. Here is how the Reference Tool Life given Optimum Spindle Speed calculation can be explained with given input values -> 8.333381 = (((0.050885*2*pi*10/0.0833333333333333)^(1/0.512942))*((1-0.512942)*(70*36+70)*(1-(0.45^((1+0.512942)/0.512942)))))/((1+0.512942)*70*(1-0.45)).

FAQ

What is Reference Tool Life given Optimum Spindle Speed?
The Reference Tool Life given Optimum Spindle Speed is a method to determine the tool Life of a Machining Tool when used under the reference condition such that the Facing Operation finishes at minimum expense and is represented as Tref = (((ns*2*pi*Ro/Vref)^(1/n))*((1-n)*(Ct*tc+Ct)*(1-(ar^((1+n)/n)))))/((1+n)*Ct*(1-ar)) or 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)). Rotational Frequency of Spindle is the number of turns made by the spindle of the Machine for cutting in one second, Outer Radius of Workpiece is the radius of the outermost surface of the workpiece, away from the machining tool, Reference Cutting Velocity is the Cutting Velocity of the tool used in the reference Machining Condition, Taylor's Tool Life Exponent is an experimental exponent that helps in quantifying the rate of Tool Wear, The Cost of a Tool is simply the cost of one tool being used for machining, Time to Change One Tool is the measure of time it takes to change one tool during machining & Workpiece Radius Ratio is the ratio of the inner radius of the workpiece to its outer radius.
How to calculate Reference Tool Life given Optimum Spindle Speed?
The Reference Tool Life given Optimum Spindle Speed is a method to determine the tool Life of a Machining Tool when used under the reference condition such that the Facing Operation finishes at minimum expense is calculated using 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)). To calculate Reference Tool Life given Optimum Spindle Speed, you need Rotational Frequency of Spindle (ns), Outer Radius of Workpiece (Ro), Reference Cutting Velocity (Vref), Taylor's Tool Life Exponent (n), Cost of a Tool (Ct), Time to Change One Tool (tc) & Workpiece Radius Ratio (ar). With our tool, you need to enter the respective value for Rotational Frequency of Spindle, Outer Radius of Workpiece, Reference Cutting Velocity, Taylor's Tool Life Exponent, Cost of a Tool, Time to Change One Tool & Workpiece Radius Ratio 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 Reference Tool Life?
In this formula, Reference Tool Life uses Rotational Frequency of Spindle, Outer Radius of Workpiece, Reference Cutting Velocity, Taylor's Tool Life Exponent, Cost of a Tool, Time to Change One Tool & Workpiece Radius Ratio. We can use 1 other way(s) to calculate the same, which is/are as follows -
  • Reference Tool Life = ((Cutting Velocity/Reference Cutting Velocity)^(1/Taylor's Tool Life Exponent))*Time Proportion of Cutting Edge Engagement*Tool Life
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