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Optimum Spindle Speed Calculator

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✖Reference Cutting Velocity Spindle Speed 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 Spindle Speed [Vss]
+10%
-10%
✖Outer Radius of Workpiece is the distance from the center of rotation to the outermost surface of the workpiece being machined.ⓘ Outer Radius of Workpiece [Ro]
+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%
✖The Cost of a Tool refers to the expenses associated with acquiring and using cutting tools used in various machining operations.ⓘ Cost of a Tool [Ct]
+10%
-10%
✖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 [Tref]
+10%
-10%
✖Workpiece Radius Ratio refers to the ratio between the initial radius and the final radius of the workpiece being machined.ⓘ Workpiece Radius Ratio [ar]
+10%
-10%
✖Time to Change One Tool refers to the duration required to replace a cutting tool with another tool during a machining operation.ⓘ Time to Change One Tool [tc]
+10%
-10%
✖Rotational Frequency of Spindle is the speed at which the spindle of a machine tool rotates during machining operations. It is typically measured in revolutions per minute.ⓘ Optimum Spindle Speed [ns]
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Formula
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Optimum Spindle Speed

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

Example
`"600rev/min"=("930230.1mm/min"/(2*pi*"1000mm"))*(((1+"0.512942")*"158.8131"*"5min"*(1-"0.45"))/((1-"0.512942")*("158.8131"*"0.6min"+"158.8131")*(1-("0.45")^((1+"0.512942")/"0.512942"))))^"0.512942"`

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Optimum Spindle Speed Solution

STEP 0: Pre-Calculation Summary
Formula Used
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
ns = (Vss/(2*pi*Ro))*(((1+n)*Ct*Tref*(1-ar))/((1-n)*(Ct*tc+Ct)*(1-ar^((1+n)/n))))^n
This formula uses 1 Constants, 8 Variables
Constants Used
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
Variables Used
Rotational Frequency of Spindle - (Measured in Hertz) - Rotational Frequency of Spindle is the speed at which the spindle of a machine tool rotates during machining operations. It is typically measured in revolutions per minute.
Reference Cutting Velocity Spindle Speed - (Measured in Meter per Second) - Reference Cutting Velocity Spindle Speed refers to a standard cutting speed used as a baseline or reference point for selecting appropriate cutting speeds for specific machining operations.
Outer Radius of Workpiece - (Measured in Meter) - Outer Radius of Workpiece is the distance from the center of rotation to the outermost surface of the workpiece being machined.
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.
Cost of a Tool - The Cost of a Tool refers to the expenses associated with acquiring and using cutting tools used in various machining operations.
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.
Workpiece Radius Ratio - Workpiece Radius Ratio refers to the ratio between the initial radius and the final radius of the workpiece being machined.
Time to Change One Tool - (Measured in Second) - Time to Change One Tool refers to the duration required to replace a cutting tool with another tool during a machining operation.
STEP 1: Convert Input(s) to Base Unit
Reference Cutting Velocity Spindle Speed: 930230.1 Millimeter per Minute --> 15.503835 Meter per Second (Check conversion ​here)
Outer Radius of Workpiece: 1000 Millimeter --> 1 Meter (Check conversion ​here)
Taylor's Tool Life Exponent: 0.512942 --> No Conversion Required
Cost of a Tool: 158.8131 --> No Conversion Required
Reference Tool Life: 5 Minute --> 300 Second (Check conversion ​here)
Workpiece Radius Ratio: 0.45 --> No Conversion Required
Time to Change One Tool: 0.6 Minute --> 36 Second (Check conversion ​here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
ns = (Vss/(2*pi*Ro))*(((1+n)*Ct*Tref*(1-ar))/((1-n)*(Ct*tc+Ct)*(1-ar^((1+n)/n))))^n --> (15.503835/(2*pi*1))*(((1+0.512942)*158.8131*300*(1-0.45))/((1-0.512942)*(158.8131*36+158.8131)*(1-0.45^((1+0.512942)/0.512942))))^0.512942
Evaluating ... ...
ns = 9.99999968740138
STEP 3: Convert Result to Output's Unit
9.99999968740138 Hertz -->599.999981244083 Revolution per Minute (Check conversion ​here)
FINAL ANSWER
599.999981244083 ≈ 600 Revolution per Minute <-- Rotational Frequency of Spindle
(Calculation completed in 00.004 seconds)
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Credits

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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 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

Optimum Spindle Speed Formula

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

Production Cost for Facing

The Total Production Cost is defined as the cumulative of all the costs of different processes in Facing Operation. This includes the cost of loading/unloading the tool, cost of setup of workpiece, machining cost, and the cost of tools used.

How to Calculate Optimum Spindle Speed?

Optimum Spindle Speed calculator uses 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 to calculate the Rotational Frequency of Spindle, Optimum spindle speed is critical for achieving efficient metal machining processes. Machinists often rely on experience, empirical data, manufacturer recommendations, and machining simulations to determine the optimum spindle speed for specific machining applications. Continuous monitoring and adjustment of spindle speed throughout the machining process help maintain optimal cutting conditions and maximize machining performance. Rotational Frequency of Spindle is denoted by ns symbol.

How to calculate Optimum Spindle Speed using this online calculator? To use this online calculator for Optimum Spindle Speed, enter Reference Cutting Velocity Spindle Speed (Vss), Outer Radius of Workpiece (Ro), Taylor's Tool Life Exponent (n), Cost of a Tool (Ct), Reference Tool Life (Tref), Workpiece Radius Ratio (ar) & Time to Change One Tool (tc) and hit the calculate button. Here is how the Optimum Spindle Speed calculation can be explained with given input values -> 36000 = (15.503835/(2*pi*1))*(((1+0.512942)*158.8131*300*(1-0.45))/((1-0.512942)*(158.8131*36+158.8131)*(1-0.45^((1+0.512942)/0.512942))))^0.512942.

FAQ

What is Optimum Spindle Speed?
Optimum spindle speed is critical for achieving efficient metal machining processes. Machinists often rely on experience, empirical data, manufacturer recommendations, and machining simulations to determine the optimum spindle speed for specific machining applications. Continuous monitoring and adjustment of spindle speed throughout the machining process help maintain optimal cutting conditions and maximize machining performance and is represented as ns = (Vss/(2*pi*Ro))*(((1+n)*Ct*Tref*(1-ar))/((1-n)*(Ct*tc+Ct)*(1-ar^((1+n)/n))))^n or 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 Spindle Speed refers to a standard cutting speed used as a baseline or reference point for selecting appropriate cutting speeds for specific machining operations, Outer Radius of Workpiece is the distance from the center of rotation to the outermost surface of the workpiece being machined, 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, The Cost of a Tool refers to the expenses associated with acquiring and using cutting tools used in various machining operations, 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, Workpiece Radius Ratio refers to the ratio between the initial radius and the final radius of the workpiece being machined & Time to Change One Tool refers to the duration required to replace a cutting tool with another tool during a machining operation.
How to calculate Optimum Spindle Speed?
Optimum spindle speed is critical for achieving efficient metal machining processes. Machinists often rely on experience, empirical data, manufacturer recommendations, and machining simulations to determine the optimum spindle speed for specific machining applications. Continuous monitoring and adjustment of spindle speed throughout the machining process help maintain optimal cutting conditions and maximize machining performance is calculated using 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. To calculate Optimum Spindle Speed, you need Reference Cutting Velocity Spindle Speed (Vss), Outer Radius of Workpiece (Ro), Taylor's Tool Life Exponent (n), Cost of a Tool (Ct), Reference Tool Life (Tref), Workpiece Radius Ratio (ar) & Time to Change One Tool (tc). With our tool, you need to enter the respective value for Reference Cutting Velocity Spindle Speed, Outer Radius of Workpiece, Taylor's Tool Life Exponent, Cost of a Tool, Reference Tool Life, Workpiece Radius Ratio & Time to Change One Tool 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 Rotational Frequency of Spindle?
In this formula, Rotational Frequency of Spindle uses Reference Cutting Velocity Spindle Speed, Outer Radius of Workpiece, Taylor's Tool Life Exponent, Cost of a Tool, Reference Tool Life, Workpiece Radius Ratio & Time to Change One Tool. We can use 2 other way(s) to calculate the same, which is/are as follows -
  • 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
  • Rotational Frequency of Spindle = Cutting Velocity/(2*pi*Instantaneous Radius for Cut)
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