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Roughness Value Formula

GoRoughness value given corner radius Formula

GoRoughness value given feed speed Formula

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Roughness Value is the arithmetic average of the absolute values of the roughness profile ordinates. Check FAQs

R = \frac{f}{4 \cdot (\cot (θ) + \cot (θ'))}

R - Roughness Value?f - Feed?θ - Working Major Cutting Edge Angle?θ' - Working Minor Cutting Edge?

Roughness Value Example

With values

With units

Only example

Here is how the Roughness Value equation looks like with Values.

Here is how the Roughness Value equation looks like with Units.

Here is how the Roughness Value equation looks like.

0.0171 = \frac{0.9}{4 \cdot (\cot (45.171) + \cot (4.69))}

0.0171mm = \frac{0.9mm}{4 \cdot (\cot (45.171°) + \cot (4.69°))}

0.0171 = \frac{0.9}{4 \cdot (\cot (45.171) + \cot (4.69))}

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Roughness Value Solution

Follow our step by step solution on how to calculate Roughness Value?

FIRST Step Consider the formula

R = \frac{f}{4 \cdot (\cot (θ) + \cot (θ'))}

Next Step Substitute values of Variables

∴

R = \frac{0.9mm}{4 \cdot (\cot (45.171°) + \cot (4.69°))}

Next Step Convert Units

∴

R = \frac{0.0009m}{4 \cdot (\cot (0.7884rad) + \cot (0.0819rad))}

Next Step Prepare to Evaluate

∴

R = \frac{0.0009}{4 \cdot (\cot (0.7884) + \cot (0.0819))}

Next Step Evaluate

∴

R = 1.70669998653583E-05m

Next Step Convert to Output's Unit

∴

R = 0.0170669998653583mm

LAST Step Rounding Answer

∴

R = 0.0171mm

Roughness Value Formula Elements

Variables

Functions

Roughness Value

Roughness Value is the arithmetic average of the absolute values of the roughness profile ordinates.

Symbol: R

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Roughness Value

Feed

The Feed is the distance as the cutting tool advances along the length of the work for every revolution of the spindle.

Symbol: f

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Feed

Working Major Cutting Edge Angle

The Working Major Cutting Edge Angle is the angle formed by the cutting edge, starting from the point where the cutting edge first engages with the workpiece.

Symbol: θ

Measurement: AngleUnit: °

Note: Value should be greater than 0.

Formulas to find Working Major Cutting Edge Angle

Working Minor Cutting Edge

The Working Minor Cutting Edge is the portion of the cutting edge that extends from the end of the primary cutting edge to the point where it effectively has no cutting action.

Symbol: θ'

Measurement: AngleUnit: °

Note: Value should be greater than 0.

Formulas to find Working Minor Cutting Edge

cot

Cotangent is a trigonometric function that is defined as the ratio of the adjacent side to the opposite side in a right triangle.

Syntax: cot(Angle)

Other Formulas to find Roughness Value

Go Roughness value given corner radius

R = 0.0321 \cdot \frac{{(f)}^{2}}{r c}

Go Roughness value given feed speed

R = \frac{0.0642 \cdot {(V f)}^{2}}{d t \cdot {(ω c)}^{2}}

Go Roughness Value of Tool

R = 0.0321 \cdot \frac{{(f)}^{2}}{r c}

Other formulas in Cutting Force and Surface Roughness category

Go Cutting Force given Rate of Energy Consumption during Machining

F c = \frac{Q c}{V c}

Go Cutting Force given Specific Cutting Energy in Machining

F c = Q sc \cdot A cs

Go Force required to remove Chip and Acting on Tool Face

F r = F rc - F p

Go Resultant Cutting Force using Force required to remove Chip

F rc = F r + F p

How to Evaluate Roughness Value?

Roughness Value evaluator uses Roughness Value = Feed/(4*(cot(Working Major Cutting Edge Angle)+cot(Working Minor Cutting Edge))) to evaluate the Roughness Value, The Roughness Value is the arithmetic average of the absolute values of the roughness profile ordinates. Roughness Value is denoted by R symbol.

How to evaluate Roughness Value using this online evaluator? To use this online evaluator for Roughness Value, enter Feed (f), Working Major Cutting Edge Angle (θ) & Working Minor Cutting Edge (θ') and hit the calculate button.

FAQs on Roughness Value

What is the formula to find Roughness Value?

The formula of Roughness Value is expressed as Roughness Value = Feed/(4*(cot(Working Major Cutting Edge Angle)+cot(Working Minor Cutting Edge))). Here is an example- 17.0593 = 0.0009/(4*(cot(0.788382152819435)+cot(0.0818559419185187))).

How to calculate Roughness Value?

With Feed (f), Working Major Cutting Edge Angle (θ) & Working Minor Cutting Edge (θ') we can find Roughness Value using the formula - Roughness Value = Feed/(4*(cot(Working Major Cutting Edge Angle)+cot(Working Minor Cutting Edge))). This formula also uses Cotangent (cot) function(s).

What are the other ways to Calculate Roughness Value?

Here are the different ways to Calculate Roughness Value-

Roughness Value=0.0321*(Feed)^2/Corner Radius of Tool
Roughness Value=(0.0642*(Feed Speed)^2)/(Diameter of Cutter*(Rotational Frequency of Cutter)^2)
Roughness Value=0.0321*(Feed)^2/Corner Radius of Tool

Can the Roughness Value be negative?

No, the Roughness Value, measured in Length cannot be negative.

Which unit is used to measure Roughness Value?

Roughness Value is usually measured using the Millimeter[mm] for Length. Meter[mm], Kilometer[mm], Decimeter[mm] are the few other units in which Roughness Value can be measured.

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Roughness Value Formula

​GoRoughness value given corner radius Formula

​GoRoughness value given feed speed Formula

Roughness Value Example

Roughness Value Solution

Roughness Value Formula Elements

Other Formulas to find Roughness Value

Other formulas in Cutting Force and Surface Roughness category

How to Evaluate Roughness Value?

FAQs on Roughness Value

Variable Name

GoRoughness value given corner radius Formula

GoRoughness value given feed speed Formula