Machining and Operating Rate given Optimum Spindle Speed Calculator

✖The Cost of a Tool is simply the cost of one tool being used for machining.ⓘ Cost of a Tool [C_t]			+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%
✖Outer Radius of Workpiece is the radius of the outermost surface of the workpiece, away from the machining tool.ⓘ Outer Radius of Workpiece [R_o]			+10% -10%
✖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 [n_s]			+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%
✖Workpiece Radius Ratio is the ratio of the inner radius of the workpiece to its outer radius.ⓘ Workpiece Radius Ratio [a_r]			+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%
✖Time to Change One Tool is the measure of time it takes to change one tool during machining.ⓘ Time to Change One Tool [t_c]			+10% -10%

✖Machining and Operating Rate is the money charged for processing on and operating machines per unit time, including overheads.ⓘ Machining and Operating Rate given Optimum Spindle Speed [M]

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Machining and Operating Rate given Optimum Spindle Speed

Formula

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

Example

`"4.5E^6"=("70"/((((((("5000mm/min"/(2*pi*"10000mm")))/"10Hz")^(1/"0.512942"))*((((1+"0.512942")/(1-"0.512942")))*((1-"0.45")/(1-(("0.45")^(("0.512942"+1)/"0.512942"))))*"5min"))))-"0.6min")`

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Machining and Operating Rate given Optimum Spindle Speed Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)
M = (C_t/(((((((V_ref/(2*pi*R_o)))/n_s)^(1/n))*((((1+n)/(1-n)))*((1-a_r)/(1-((a_r)^((n+1)/n))))*T_ref))))-t_c)
This formula uses 1 Constants, 9 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Machining and Operating Rate - Machining and Operating Rate is the money charged for processing on and operating machines per unit time, including overheads.
Cost of a Tool - The Cost of a Tool is simply the cost of one tool being used for machining.
Reference Cutting Velocity - (Measured in Meter per Second) - Reference Cutting Velocity is the Cutting Velocity of the tool used in the reference Machining Condition.
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.
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.
Taylor's Tool Life Exponent - Taylor's Tool Life Exponent is an experimental exponent that helps in quantifying the rate of Tool Wear.
Workpiece Radius Ratio - Workpiece Radius Ratio is the ratio of the inner radius of the workpiece to its outer radius.
Reference Tool Life - (Measured in Second) - Reference Tool Life is the Tool Life of the tool obtained in the reference Machining Condition.
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.

STEP 1: Convert Input(s) to Base Unit

Cost of a Tool: 70 --> No Conversion Required
Reference Cutting Velocity: 5000 Millimeter per Minute --> 0.0833333333333333 Meter per Second (Check conversion here)
Outer Radius of Workpiece: 10000 Millimeter --> 10 Meter (Check conversion here)
Rotational Frequency of Spindle: 10 Hertz --> 10 Hertz No Conversion Required
Taylor's Tool Life Exponent: 0.512942 --> No Conversion Required
Workpiece Radius Ratio: 0.45 --> No Conversion Required
Reference Tool Life: 5 Minute --> 300 Second (Check conversion here)
Time to Change One Tool: 0.6 Minute --> 36 Second (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

M = (C_t/(((((((V_ref/(2*pi*R_o)))/n_s)^(1/n))*((((1+n)/(1-n)))*((1-a_r)/(1-((a_r)^((n+1)/n))))*T_ref))))-t_c) --> (70/(((((((0.0833333333333333/(2*pi*10)))/10)^(1/0.512942))*((((1+0.512942)/(1-0.512942)))*((1-0.45)/(1-((0.45)^((0.512942+1)/0.512942))))*300))))-36)

Evaluating ... ...

M = 4478602.72602514

STEP 3: Convert Result to Output's Unit

4478602.72602514 --> No Conversion Required

FINAL ANSWER

4478602.72602514 ≈ 4.5E+6 <-- Machining and Operating Rate

(Calculation completed in 00.004 seconds)

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Home » Engineering » Production Engineering » Metal Machining » Facing Operation » Machine Tools and Operations » Cutting Speed » Machining and Operating Rate given Optimum Spindle Speed

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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)^(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

Machining and Operating Rate given Optimum Spindle Speed Formula

Machining Time Estimation Methods

Commonly used Machining Time Estimation Methods are:
1. By estimation
2. By Timing
3. By Comparison
4. By the sum of elementary pre-defined times

How to Calculate Machining and Operating Rate given Optimum Spindle Speed?

Machining and Operating Rate given Optimum Spindle Speed calculator uses 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) to calculate the Machining and Operating Rate, The Machining and Operating Rate given Optimum Spindle Speed is a method to determine the maximum amount that can be spent on Machining and Operating when the resources to be used are strictly bounded for minimum production cost. Machining and Operating Rate is denoted by M symbol.

How to calculate Machining and Operating Rate given Optimum Spindle Speed using this online calculator? To use this online calculator for Machining and Operating Rate given Optimum Spindle Speed, enter Cost of a Tool (C_t), Reference Cutting Velocity (V_ref), Outer Radius of Workpiece (R_o), Rotational Frequency of Spindle (n_s), Taylor's Tool Life Exponent (n), Workpiece Radius Ratio (a_r), Reference Tool Life (T_ref) & Time to Change One Tool (t_c) and hit the calculate button. Here is how the Machining and Operating Rate given Optimum Spindle Speed calculation can be explained with given input values -> 7.3E+6 = (70/(((((((0.0833333333333333/(2*pi*10)))/10)^(1/0.512942))*((((1+0.512942)/(1-0.512942)))*((1-0.45)/(1-((0.45)^((0.512942+1)/0.512942))))*300))))-36).

FAQ

What is Machining and Operating Rate given Optimum Spindle Speed?

The Machining and Operating Rate given Optimum Spindle Speed is a method to determine the maximum amount that can be spent on Machining and Operating when the resources to be used are strictly bounded for minimum production cost and is represented as M = (C_t/(((((((V_ref/(2*pi*R_o)))/n_s)^(1/n))*((((1+n)/(1-n)))*((1-a_r)/(1-((a_r)^((n+1)/n))))*T_ref))))-t_c) or 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). The Cost of a Tool is simply the cost of one tool being used for machining, Reference Cutting Velocity is the Cutting Velocity of the tool used in the reference Machining Condition, Outer Radius of Workpiece is the radius of the outermost surface of the workpiece, away from the machining tool, Rotational Frequency of Spindle is the number of turns made by the spindle of the Machine for cutting in one second, Taylor's Tool Life Exponent is an experimental exponent that helps in quantifying the rate of Tool Wear, Workpiece Radius Ratio is the ratio of the inner radius of the workpiece to its outer radius, Reference Tool Life is the Tool Life of the tool obtained in the reference Machining Condition & Time to Change One Tool is the measure of time it takes to change one tool during machining.

How to calculate Machining and Operating Rate given Optimum Spindle Speed?

The Machining and Operating Rate given Optimum Spindle Speed is a method to determine the maximum amount that can be spent on Machining and Operating when the resources to be used are strictly bounded for minimum production cost is calculated using 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). To calculate Machining and Operating Rate given Optimum Spindle Speed, you need Cost of a Tool (C_t), Reference Cutting Velocity (V_ref), Outer Radius of Workpiece (R_o), Rotational Frequency of Spindle (n_s), Taylor's Tool Life Exponent (n), Workpiece Radius Ratio (a_r), Reference Tool Life (T_ref) & Time to Change One Tool (t_c). With our tool, you need to enter the respective value for Cost of a Tool, Reference Cutting Velocity, Outer Radius of Workpiece, Rotational Frequency of Spindle, Taylor's Tool Life Exponent, Workpiece Radius Ratio, Reference Tool Life & 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.

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