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Outside Radius of Workpiece given Optimum Spindle Speed Formula

GoOutside Radius of Workpiece given Instantaneous Radius for Cut Formula

GoOutside Radius given Workpiece Radius Ratio Formula

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Outside Radius of the Workpiece is the radius of the outermost surface of the workpiece, away from the machining tool. Check FAQs

r o = (\frac{V ref}{2 \cdot π \cdot ω s}) \cdot {(\frac{(1 + n) \cdot C t \cdot L ref \cdot (1 - R w)}{(1 - n) \cdot (C t \cdot t c + C t) \cdot (1 - ({R w}^{\frac{1 + n}{n}}))})}^{n}

r_o - Outside Radius of The Workpiece?V_ref - Reference Cutting Velocity?ω_s - Rotational Frequency of Spindle?n - Taylor's Tool Life Exponent?C_t - Cost of A Tool?L_ref - Reference Tool Life?R_w - Workpiece Radius Ratio?t_c - Time to Change One Tool?π - Archimedes' constant?

Outside Radius of Workpiece given Optimum Spindle Speed Example

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Here is how the Outside Radius of Workpiece given Optimum Spindle Speed equation looks like with Values.

Here is how the Outside Radius of Workpiece given Optimum Spindle Speed equation looks like with Units.

Here is how the Outside Radius of Workpiece given Optimum Spindle Speed equation looks like.

59036.5702 = (\frac{1050}{2 \cdot 3.1416 \cdot 10}) \cdot {(\frac{(1 + 0.5) \cdot 70 \cdot 5 \cdot (1 - 0.595)}{(1 - 0.5) \cdot (70 \cdot 0.6 + 70) \cdot (1 - ({0.595}^{\frac{1 + 0.5}{0.5}}))})}^{0.5}

59036.5702mm = (\frac{1050m/s}{2 \cdot 3.1416 \cdot 10Hz}) \cdot {(\frac{(1 + 0.5) \cdot 70 \cdot 5min \cdot (1 - 0.595)}{(1 - 0.5) \cdot (70 \cdot 0.6min + 70) \cdot (1 - ({0.595}^{\frac{1 + 0.5}{0.5}}))})}^{0.5}

59036.5702 = (\frac{1050}{2 \cdot 3.1416 \cdot 10}) \cdot {(\frac{(1 + 0.5) \cdot 70 \cdot 5 \cdot (1 - 0.595)}{(1 - 0.5) \cdot (70 \cdot 0.6 + 70) \cdot (1 - ({0.595}^{\frac{1 + 0.5}{0.5}}))})}^{0.5}

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Outside Radius of Workpiece given Optimum Spindle Speed Solution

Follow our step by step solution on how to calculate Outside Radius of Workpiece given Optimum Spindle Speed?

FIRST Step Consider the formula

r o = (\frac{V ref}{2 \cdot π \cdot ω s}) \cdot {(\frac{(1 + n) \cdot C t \cdot L ref \cdot (1 - R w)}{(1 - n) \cdot (C t \cdot t c + C t) \cdot (1 - ({R w}^{\frac{1 + n}{n}}))})}^{n}

Next Step Substitute values of Variables

∴

r o = (\frac{1050m/s}{2 \cdot π \cdot 10Hz}) \cdot {(\frac{(1 + 0.5) \cdot 70 \cdot 5min \cdot (1 - 0.595)}{(1 - 0.5) \cdot (70 \cdot 0.6min + 70) \cdot (1 - ({0.595}^{\frac{1 + 0.5}{0.5}}))})}^{0.5}

Next Step Substitute values of Constants

∴

r o = (\frac{1050m/s}{2 \cdot 3.1416 \cdot 10Hz}) \cdot {(\frac{(1 + 0.5) \cdot 70 \cdot 5min \cdot (1 - 0.595)}{(1 - 0.5) \cdot (70 \cdot 0.6min + 70) \cdot (1 - ({0.595}^{\frac{1 + 0.5}{0.5}}))})}^{0.5}

Next Step Convert Units

∴

r o = (\frac{1050m/s}{2 \cdot 3.1416 \cdot 10Hz}) \cdot {(\frac{(1 + 0.5) \cdot 70 \cdot 300s \cdot (1 - 0.595)}{(1 - 0.5) \cdot (70 \cdot 36s + 70) \cdot (1 - ({0.595}^{\frac{1 + 0.5}{0.5}}))})}^{0.5}

Next Step Prepare to Evaluate

∴

r o = (\frac{1050}{2 \cdot 3.1416 \cdot 10}) \cdot {(\frac{(1 + 0.5) \cdot 70 \cdot 300 \cdot (1 - 0.595)}{(1 - 0.5) \cdot (70 \cdot 36 + 70) \cdot (1 - ({0.595}^{\frac{1 + 0.5}{0.5}}))})}^{0.5}

Next Step Evaluate

∴

r o = 59.036570172542m

Next Step Convert to Output's Unit

∴

r o = 59036.570172542mm

LAST Step Rounding Answer

∴

r o = 59036.5702mm

Outside Radius of Workpiece given Optimum Spindle Speed Formula Elements

Variables

Constants

Outside Radius of The Workpiece

Outside Radius of the Workpiece is the radius of the outermost surface of the workpiece, away from the machining tool.

Symbol: r_o

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Reference Cutting Velocity

Reference Cutting Velocity is the cutting velocity of the tool used in the reference machining Condition.

Symbol: V_ref

Measurement: SpeedUnit: m/s

Note: Value should be greater than 0.

Rotational Frequency of Spindle

Rotational Frequency of Spindle is the number of turns made by the spindle of the Machine for cutting in one second.

Symbol: ω_s

Measurement: FrequencyUnit: Hz

Note: Value should be greater than 0.

Taylor's Tool Life Exponent

Taylor's Tool Life Exponent is an experimental exponent that helps in quantifying the rate of tool wear.

Symbol: n

Measurement: NAUnit: Unitless

Note: Value should be less than 1.

Cost of A Tool

The Cost of A Tool is simply the cost of one tool being used for machining.

Symbol: C_t

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Reference Tool Life

Reference Tool Life is the Tool Life of the tool obtained in the reference machining condition.

Symbol: L_ref

Measurement: TimeUnit: min

Note: Value should be greater than 0.

Workpiece Radius Ratio

Workpiece Radius Ratio is the ratio of the inner radius of the workpiece to its outer radius.

Symbol: R_w

Measurement: NAUnit: Unitless

Note: Value should be less than 1.

Time to Change One Tool

Time to Change One Tool is the measure of time it takes to change one tool during machining.

Symbol: t_c

Measurement: TimeUnit: min

Note: Value should be greater than 0.

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

Credits

Created by Kumar Siddhant

Indian Institute of Information Technology, Design and Manufacturing (IIITDM), Jabalpur

Kumar Siddhant has created this Formula and 400+ more formulas!

Verified by Parul Keshav

National Institute of Technology (NIT), Srinagar

Parul Keshav has verified this Formula and 400+ more formulas!

Other Formulas to find Outside Radius of The Workpiece

Go Outside Radius of Workpiece given Instantaneous Radius for Cut

r o = r + ω s \cdot f \cdot t′

Go Outside Radius given Workpiece Radius Ratio

r o = \frac{r i}{R w}

Other formulas in Instantaneous Radius category

Go Instantaneous Radius for Cut given Cutting Speed

r = \frac{V}{2 \cdot π \cdot ω s}

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

r = \frac{V ref \cdot {(W r \cdot \frac{L ref}{W max})}^{n}}{2 \cdot π \cdot ω s}

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

Outside Radius of Workpiece given Optimum Spindle Speed evaluator 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 evaluate 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 evaluate Outside Radius of Workpiece given Optimum Spindle Speed using this online evaluator? To use this online evaluator 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.

FAQs on Outside Radius of Workpiece given Optimum Spindle Speed

What is the formula to find Outside Radius of Workpiece given Optimum Spindle Speed?

The formula of Outside Radius of Workpiece given Optimum Spindle Speed is expressed as 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. Here is an example- 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.

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

With 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) we can find Outside Radius of Workpiece given Optimum Spindle Speed using the formula - 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. This formula also uses Archimedes' constant .

What are the other ways to Calculate Outside Radius of The Workpiece?

Here are the different ways to Calculate Outside Radius of The Workpiece-

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

Can the Outside Radius of Workpiece given Optimum Spindle Speed be negative?

No, the Outside Radius of Workpiece given Optimum Spindle Speed, measured in Length cannot be negative.

Which unit is used to measure Outside Radius of Workpiece given Optimum Spindle Speed?

Outside Radius of Workpiece given Optimum Spindle Speed is usually measured using the Millimeter[mm] for Length. Meter[mm], Kilometer[mm], Decimeter[mm] are the few other units in which Outside Radius of Workpiece given Optimum Spindle Speed can be measured.

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Outside Radius of Workpiece given Optimum Spindle Speed Formula

​GoOutside Radius of Workpiece given Instantaneous Radius for Cut Formula

​GoOutside Radius given Workpiece Radius Ratio Formula

Outside Radius of Workpiece given Optimum Spindle Speed Example

Outside Radius of Workpiece given Optimum Spindle Speed Solution

Outside Radius of Workpiece given Optimum Spindle Speed Formula Elements

Credits

Other Formulas to find Outside Radius of The Workpiece

Other formulas in Instantaneous Radius category

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

FAQs on Outside Radius of Workpiece given Optimum Spindle Speed

Variable Name

GoOutside Radius of Workpiece given Instantaneous Radius for Cut Formula

GoOutside Radius given Workpiece Radius Ratio Formula