FormulaDen.com

Physics Chemistry Math Chemical Engineering Civil Electrical Electronics Electronics and Instrumentation Materials Science Mechanical Production Engineering Financial Health

Rotational Frequency of Spindle given Rate of Increase of Wear-Land Formula

Fx Copy

LaTeX Copy

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

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

n_s - Rotational Frequency of Spindle?V_ref - Reference Cutting Velocity?V_ratio - Rate of Increase of Wear Land Width?T_ref - Reference Tool Life?W_max - Maximum Wear Land Width?n - Taylor's Tool Life Exponent?r - Instantaneous Radius For Cut?π - Archimedes' constant?

Rotational Frequency of Spindle given Rate of Increase of Wear-Land Example

With values

With units

Only example

Here is how the Rotational Frequency of Spindle given Rate of Increase of Wear-Land equation looks like with Values.

Here is how the Rotational Frequency of Spindle given Rate of Increase of Wear-Land equation looks like with Units.

Here is how the Rotational Frequency of Spindle given Rate of Increase of Wear-Land equation looks like.

10 = \frac{5000 \cdot {(0.16 \cdot \frac{5}{0.3125})}^{0.5}}{2 \cdot 3.1416 \cdot 2.1221}

10rad/s = \frac{5000mm/min \cdot {(0.16mm/min \cdot \frac{5min}{0.3125mm})}^{0.5}}{2 \cdot 3.1416 \cdot 2.1221mm}

10 = \frac{5000 \cdot {(0.16 \cdot \frac{5}{0.3125})}^{0.5}}{2 \cdot 3.1416 \cdot 2.1221}

Tip: Use pencil () icon above to edit Input Values and Units.

Calculate

Recalculate

Solution

Copy

Reset

You are here -

Home » Engineering » Production Engineering » Metal Machining » Rotational Frequency of Spindle given Rate of Increase of Wear-Land

Rotational Frequency of Spindle given Rate of Increase of Wear-Land Solution

Follow our step by step solution on how to calculate Rotational Frequency of Spindle given Rate of Increase of Wear-Land?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

n s = \frac{5000mm/min \cdot {(0.16mm/min \cdot \frac{5min}{0.3125mm})}^{0.5}}{2 \cdot π \cdot 2.1221mm}

Next Step Substitute values of Constants

∴

n s = \frac{5000mm/min \cdot {(0.16mm/min \cdot \frac{5min}{0.3125mm})}^{0.5}}{2 \cdot 3.1416 \cdot 2.1221mm}

Next Step Convert Units

∴

n s = \frac{0.0833m/s \cdot {(2.7E-6m/s \cdot \frac{300s}{0.0003m})}^{0.5}}{2 \cdot 3.1416 \cdot 0.0021m}

Next Step Prepare to Evaluate

∴

n s = \frac{0.0833 \cdot {(2.7E-6 \cdot \frac{300}{0.0003})}^{0.5}}{2 \cdot 3.1416 \cdot 0.0021}

Next Step Evaluate

∴

n s = 10.0000042783418rad/s

LAST Step Rounding Answer

∴

n s = 10rad/s

Rotational Frequency of Spindle given Rate of Increase of Wear-Land Formula Elements

Variables

Constants

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: n_s

Measurement: Angular VelocityUnit: rad/s

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: mm/min

Note: Value should be greater than 0.

Rate of Increase of Wear Land Width

Rate of Increase of Wear Land Width is the increase in the width of the region where wear occurs in a tool per unit time.

Symbol: V_ratio

Measurement: SpeedUnit: mm/min

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: T_ref

Measurement: TimeUnit: min

Note: Value should be greater than 0.

Maximum Wear Land Width

Maximum Wear Land Width is the maximum width of the region where wear occurs in a tool.

Symbol: W_max

Measurement: LengthUnit: mm

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.

Instantaneous Radius For Cut

Instantaneous Radius For Cut is the radius of the workpiece surface currently being machined.

Symbol: r

Measurement: LengthUnit: mm

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 in Wear Land category

Go Maximum Wear-Land Width

W max = L w \cdot \frac{T}{t m}

Go Increase in Wear-Land Width per Component

L w = W max \cdot \frac{t m}{T}

How to Evaluate Rotational Frequency of Spindle given Rate of Increase of Wear-Land?

Rotational Frequency of Spindle given Rate of Increase of Wear-Land evaluator uses Rotational Frequency of Spindle = (Reference Cutting Velocity*(Rate of Increase of Wear Land Width*Reference Tool Life/Maximum Wear Land Width)^Taylor's Tool Life Exponent)/(2*pi*Instantaneous Radius For Cut) to evaluate the Rotational Frequency of Spindle, The Rotational Frequency of Spindle given Rate of Increase of Wear-Land is a method to determine the required frequency of rotation of the Spindle of a Machining Tool when the Rate of Increase of Wear-Land Width is given. Rotational Frequency of Spindle is denoted by n_s symbol.

How to evaluate Rotational Frequency of Spindle given Rate of Increase of Wear-Land using this online evaluator? To use this online evaluator for Rotational Frequency of Spindle given Rate of Increase of Wear-Land, enter Reference Cutting Velocity (V_ref), Rate of Increase of Wear Land Width (V_ratio), Reference Tool Life (T_ref), Maximum Wear Land Width (W_max), Taylor's Tool Life Exponent (n) & Instantaneous Radius For Cut (r) and hit the calculate button.

FAQs on Rotational Frequency of Spindle given Rate of Increase of Wear-Land

What is the formula to find Rotational Frequency of Spindle given Rate of Increase of Wear-Land?

The formula of Rotational Frequency of Spindle given Rate of Increase of Wear-Land is expressed as Rotational Frequency of Spindle = (Reference Cutting Velocity*(Rate of Increase of Wear Land Width*Reference Tool Life/Maximum Wear Land Width)^Taylor's Tool Life Exponent)/(2*pi*Instantaneous Radius For Cut). Here is an example- 10 = (0.0833333333333333*(2.66666666666667E-06*300/0.0003125)^0.5)/(2*pi*0.002122065).

How to calculate Rotational Frequency of Spindle given Rate of Increase of Wear-Land?

With Reference Cutting Velocity (V_ref), Rate of Increase of Wear Land Width (V_ratio), Reference Tool Life (T_ref), Maximum Wear Land Width (W_max), Taylor's Tool Life Exponent (n) & Instantaneous Radius For Cut (r) we can find Rotational Frequency of Spindle given Rate of Increase of Wear-Land using the formula - Rotational Frequency of Spindle = (Reference Cutting Velocity*(Rate of Increase of Wear Land Width*Reference Tool Life/Maximum Wear Land Width)^Taylor's Tool Life Exponent)/(2*pi*Instantaneous Radius For Cut). This formula also uses Archimedes' constant .

Can the Rotational Frequency of Spindle given Rate of Increase of Wear-Land be negative?

No, the Rotational Frequency of Spindle given Rate of Increase of Wear-Land, measured in Angular Velocity cannot be negative.

Which unit is used to measure Rotational Frequency of Spindle given Rate of Increase of Wear-Land?

Rotational Frequency of Spindle given Rate of Increase of Wear-Land is usually measured using the Radian per Second[rad/s] for Angular Velocity. Radian per Day[rad/s], Radian per Hour[rad/s], Radian per Minute[rad/s] are the few other units in which Rotational Frequency of Spindle given Rate of Increase of Wear-Land can be measured.

Spanish French German Russian Italian Portuguese Polish Dutch

Let Others Know

✖

Facebook

Twitter

Copied!

: Value
: Unit

Rotational Frequency of Spindle given Rate of Increase of Wear-Land Formula

Rotational Frequency of Spindle given Rate of Increase of Wear-Land Example

Rotational Frequency of Spindle given Rate of Increase of Wear-Land Solution

Rotational Frequency of Spindle given Rate of Increase of Wear-Land Formula Elements

Credits

Other formulas in Wear Land category

How to Evaluate Rotational Frequency of Spindle given Rate of Increase of Wear-Land?

FAQs on Rotational Frequency of Spindle given Rate of Increase of Wear-Land

Variable Name