Outside Radius of Workpiece given Optimum Spindle Speed Calculator

✖Reference Cutting Velocity is the cutting velocity of the tool used in the reference machining Condition.ⓘ Reference Cutting Velocity [V_ref]			+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 [ω_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%
✖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 [L_ref]			+10% -10%
✖Workpiece Radius Ratio is the ratio of the inner radius of the workpiece to its outer radius.ⓘ Workpiece Radius Ratio [R_w]			+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%

✖Outside Radius of the Workpiece is the radius of the outermost surface of the workpiece, away from the machining tool.ⓘ Outside Radius of Workpiece given Optimum Spindle Speed [r_o]

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Outside Radius of Workpiece given Optimum Spindle Speed Solution

STEP 0: Pre-Calculation Summary

Formula Used

Outside Radius of The Workpiece = (Reference Cutting Velocity/(2*pi*Rotational Frequency of Spindle))*(((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
r_o = (V_ref/(2*pi*ω_s))*(((1+n)*C_t*L_ref*(1-R_w))/((1-n)*(C_t*t_c+C_t)*(1-(R_w^((1+n)/n)))))^n
This formula uses 1 Constants, 8 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

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.
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.
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

Reference Cutting Velocity: 1050 Meter per Second --> 1050 Meter per Second No Conversion Required
Rotational Frequency of Spindle: 10 Hertz --> 10 Hertz No Conversion Required
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: 0.595 --> 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

r_o = (V_ref/(2*pi*ω_s))*(((1+n)*C_t*L_ref*(1-R_w))/((1-n)*(C_t*t_c+C_t)*(1-(R_w^((1+n)/n)))))^n --> (1050/(2*pi*10))*(((1+0.5)*70*300*(1-0.595))/((1-0.5)*(70*36+70)*(1-(0.595^((1+0.5)/0.5)))))^0.5

Evaluating ... ...

r_o = 59.036570172542

STEP 3: Convert Result to Output's Unit

59.036570172542 Meter -->59036.570172542 Millimeter (Check conversion here)

FINAL ANSWER

59036.570172542 ≈ 59036.57 Millimeter <-- Outside Radius of The Workpiece

(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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< Instantaneous Radius Calculators

Instantaneous Radius for Cut given Rate of Increase of Wear-Land

LaTeX Go Instantaneous Radius For Cut = (Reference Cutting Velocity*(Rate of Increase of Wear Land Width*Reference Tool Life/Maximum Wear Land Width)^Taylor's Tool Life Exponent)/(2*pi*Rotational Frequency of Spindle)

Feed given Instantaneous Radius for Cut

LaTeX Go Feed = (Outside Radius of The Workpiece-Instantaneous Radius For Cut)/(Rotational Frequency of Spindle*Process Time)

Instantaneous Radius for Cut

LaTeX Go Instantaneous Radius For Cut = Outside Radius of The Workpiece-Rotational Frequency of Spindle*Feed*Process Time

Instantaneous Radius for Cut given Cutting Speed

LaTeX Go Instantaneous Radius For Cut = Cutting Velocity/(2*pi*Rotational Frequency of Spindle)

Outside Radius of Workpiece given Optimum Spindle Speed Formula

LaTeX Go

What causes flank wear?

Flank Wear is most commonly caused due to abrasive wear of the cutting edge against the machined surface. Flank Wear generally occurs when the speed of cutting is very high. It causes many losses but one of the most concerning is the increased roughness of the surface of the final product.

How to Calculate Outside Radius of Workpiece given Optimum Spindle Speed?

Outside Radius of Workpiece given Optimum Spindle Speed calculator uses Outside Radius of The Workpiece = (Reference Cutting Velocity/(2*pi*Rotational Frequency of Spindle))*(((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 Outside Radius of The Workpiece, The Outside Radius of Workpiece given Optimum Spindle Speed is a method to determine the radius of the outermost surface of the workpiece when the Facing Operation has to be finished at minimum expense. Outside Radius of The Workpiece is denoted by r_o symbol.

How to calculate Outside Radius of Workpiece given Optimum Spindle Speed using this online calculator? To use this online calculator for Outside Radius of Workpiece given Optimum Spindle Speed, enter Reference Cutting Velocity (V_ref), Rotational Frequency of Spindle (ω_s), Taylor's Tool Life Exponent (n), Cost of A Tool (C_t), Reference Tool Life (L_ref), Workpiece Radius Ratio (R_w) & Time to Change One Tool (t_c) and hit the calculate button. Here is how the Outside Radius of Workpiece given Optimum Spindle Speed calculation can be explained with given input values -> 984000 = (1050/(2*pi*10))*(((1+0.5)*70*300*(1-0.595))/((1-0.5)*(70*36+70)*(1-(0.595^((1+0.5)/0.5)))))^0.5.

FAQ

What is Outside Radius of Workpiece given Optimum Spindle Speed?

The Outside Radius of Workpiece given Optimum Spindle Speed is a method to determine the radius of the outermost surface of the workpiece when the Facing Operation has to be finished at minimum expense and is represented as r_o = (V_ref/(2*pi*ω_s))*(((1+n)*C_t*L_ref*(1-R_w))/((1-n)*(C_t*t_c+C_t)*(1-(R_w^((1+n)/n)))))^n or Outside Radius of The Workpiece = (Reference Cutting Velocity/(2*pi*Rotational Frequency of Spindle))*(((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 is the cutting velocity of the tool used in the reference machining Condition, 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, 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 Outside Radius of Workpiece given Optimum Spindle Speed?

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

In this formula, Outside Radius of The Workpiece uses Reference Cutting Velocity, Rotational Frequency of Spindle, Taylor's Tool Life Exponent, Cost of A Tool, Reference Tool Life, Workpiece Radius Ratio & Time to Change One Tool. We can use 3 other way(s) to calculate the same, which is/are as follows -

Outside Radius of The Workpiece = Instantaneous Radius For Cut+Rotational Frequency of Spindle*Feed*Process Time
Outside Radius of The Workpiece = Inner Radius of Workpiece/Workpiece Radius Ratio
Outside Radius of The Workpiece = (Cutting Velocity/(2*pi*Rotational Frequency of Spindle))+Rotational Frequency of Spindle*Feed*Process Time

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