Reference Cutting Velocity given Optimum Spindle Speed Calculator

✖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%
✖Outside Radius of the Workpiece is the radius of the outermost surface of the workpiece, away from the machining tool.ⓘ Outside Radius of The Workpiece [r_o]			+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 [C_t]			+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%
✖Workpiece Radius Ratio is the ratio of the inner radius of the workpiece to its outer radius.ⓘ Workpiece Radius Ratio [a_r]			+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%

✖Reference Cutting Velocity is the Cutting Velocity of the tool used in the reference Machining Condition.ⓘ Reference Cutting Velocity given Optimum Spindle Speed [V_ref]

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Reference Cutting Velocity given Optimum Spindle Speed

Formula

`"V"_{"ref"} = "n"_{"s"}*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

`"19595.92mm/min"="0.17684Hz"*2*pi*"1127.726mm"/((((1+"0.5")*"70"*"5min"*(1-"0.45"))/((1-"0.5")*("70"*"0.6min"+"70")*(1-(("0.45")^((1+"0.5")/"0.5")))))^"0.5")`

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Reference Cutting Velocity given Optimum Spindle Speed Solution

STEP 0: Pre-Calculation Summary

Formula Used

Reference Cutting Velocity = Rotational Frequency of Spindle*2*pi*Outside Radius of The 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)
V_ref = n_s*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)
This formula uses 1 Constants, 8 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Reference Cutting Velocity - (Measured in Meter per Second) - Reference Cutting Velocity is the Cutting Velocity of the tool used 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.
Outside Radius of The Workpiece - (Measured in Meter) - Outside Radius of the Workpiece is the radius of the outermost surface of the workpiece, away from the machining tool.
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.
Reference Tool Life - (Measured in Second) - Reference Tool Life is the Tool Life of the tool obtained in the reference Machining Condition.
Workpiece Radius Ratio - Workpiece Radius Ratio is the ratio of the inner radius of the workpiece to its outer radius.
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

Rotational Frequency of Spindle: 0.17684 Hertz --> 0.17684 Hertz No Conversion Required
Outside Radius of The Workpiece: 1127.726 Millimeter --> 1.127726 Meter (Check conversion here)
Taylor's Tool Life Exponent: 0.5 --> No Conversion Required
Cost of A Tool: 70 --> 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

V_ref = n_s*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) --> 0.17684*2*pi*1.127726/((((1+0.5)*70*300*(1-0.45))/((1-0.5)*(70*36+70)*(1-(0.45^((1+0.5)/0.5)))))^0.5)

Evaluating ... ...

V_ref = 0.326598592889521

STEP 3: Convert Result to Output's Unit

0.326598592889521 Meter per Second -->19595.9155733712 Millimeter per Minute (Check conversion here)

FINAL ANSWER

19595.9155733712 ≈ 19595.92 Millimeter per Minute <-- Reference Cutting Velocity

(Calculation completed in 00.004 seconds)

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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*Outside Radius of the 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*Outside Radius of the 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*Outside Radius of The 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*Outside Radius of the 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*Outside Radius of the 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)

Optimum Spindle Speed given Tool Changing Cost

Go Rotational Frequency of Spindle = (Reference Cutting Velocity/(2*pi*Outside Radius of the 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 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

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

Feed given Instantaneous Cutting Speed

Go Feed = (Outside Radius of the 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*(Outside Radius of The 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 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)

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

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 Cutting Velocity given Optimum Spindle Speed Formula

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 Cutting Velocity given Optimum Spindle Speed?

Reference Cutting Velocity given Optimum Spindle Speed calculator uses Reference Cutting Velocity = Rotational Frequency of Spindle*2*pi*Outside Radius of The 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 Reference Cutting Velocity, The Reference Cutting Velocity given Optimum Spindle Speed is a method to determine the Cutting Velocity for the reference condition when the Facing Operation has to be finished at minimum expense. Reference Cutting Velocity is denoted by V_ref symbol.

How to calculate Reference Cutting Velocity given Optimum Spindle Speed using this online calculator? To use this online calculator for Reference Cutting Velocity given Optimum Spindle Speed, enter Rotational Frequency of Spindle (n_s), Outside Radius of The Workpiece (r_o), Taylor's Tool Life Exponent (n), Cost of A Tool (C_t), Reference Tool Life (T_ref), Workpiece Radius Ratio (a_r) & Time to Change One Tool (t_c) and hit the calculate button. Here is how the Reference Cutting Velocity given Optimum Spindle Speed calculation can be explained with given input values -> 1.2E+9 = 0.17684*2*pi*1.127726/((((1+0.5)*70*300*(1-0.45))/((1-0.5)*(70*36+70)*(1-(0.45^((1+0.5)/0.5)))))^0.5).

FAQ

What is Reference Cutting Velocity given Optimum Spindle Speed?

The Reference Cutting Velocity given Optimum Spindle Speed is a method to determine the Cutting Velocity for the reference condition when the Facing Operation has to be finished at minimum expense and is represented as V_ref = n_s*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) or Reference Cutting Velocity = Rotational Frequency of Spindle*2*pi*Outside Radius of The 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). Rotational Frequency of Spindle is the number of turns made by the spindle of the Machine for cutting in one second, Outside Radius of the Workpiece is the radius of the outermost surface of the workpiece, away from the machining tool, 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, Reference Tool Life is the Tool Life of the tool obtained in the reference Machining Condition, Workpiece Radius Ratio is the ratio of the inner radius of the workpiece to its outer radius & Time to Change One Tool is the measure of time it takes to change one tool during machining.

How to calculate Reference Cutting Velocity given Optimum Spindle Speed?

The Reference Cutting Velocity given Optimum Spindle Speed is a method to determine the Cutting Velocity for the reference condition when the Facing Operation has to be finished at minimum expense is calculated using Reference Cutting Velocity = Rotational Frequency of Spindle*2*pi*Outside Radius of The 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 Reference Cutting Velocity given Optimum Spindle Speed, you need Rotational Frequency of Spindle (n_s), Outside Radius of The Workpiece (r_o), Taylor's Tool Life Exponent (n), Cost of A Tool (C_t), Reference Tool Life (T_ref), Workpiece Radius Ratio (a_r) & Time to Change One Tool (t_c). With our tool, you need to enter the respective value for Rotational Frequency of Spindle, Outside Radius of The 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 Reference Cutting Velocity?

In this formula, Reference Cutting Velocity uses Rotational Frequency of Spindle, Outside Radius of The 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 -

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

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