Roughness Value Calculator

✖The Feed is the distance the cutting tool advances along the length of the work for every revolution of the spindle.ⓘ Feed [f]			+10% -10%
✖The Working Major Cutting-edge Angle is that entire part of the cutting edge which commences at the point where the working cutting edge is zero.ⓘ Working Major Cutting-Edge Angle [K_re]			+10% -10%
✖Working Minor Cutting Edge is the remainder of the cutting edge, where present, commences at the point on the cutting edge where is zero.ⓘ Working Minor Cutting Edge [K_re']			+10% -10%

✖Roughness Value is the arithmetic average of the absolute values of the roughness profile ordinates.ⓘ Roughness Value [R_a]

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Formula

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Roughness Value

Formula

`"R"_{"a"} = "f"/(4*(cot("K"_{"re"})+cot(("K"_{"re"}"'"))))`

Example

`"0.017059mm"="0.9mm"/(4*(cot("45°")+cot("4.69°")))`

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Roughness Value Solution

STEP 0: Pre-Calculation Summary

Formula Used

Roughness Value = Feed/(4*(cot(Working Major Cutting-Edge Angle)+cot(Working Minor Cutting Edge)))
R_a = f/(4*(cot(K_re)+cot(K_re')))
This formula uses 1 Functions, 4 Variables

Functions Used

cot - Cotangent is a trigonometric function that is defined as the ratio of the adjacent side to the opposite side in a right triangle., cot(Angle)

Variables Used

Roughness Value - (Measured in Meter) - Roughness Value is the arithmetic average of the absolute values of the roughness profile ordinates.
Feed - (Measured in Meter) - The Feed is the distance the cutting tool advances along the length of the work for every revolution of the spindle.
Working Major Cutting-Edge Angle - (Measured in Radian) - The Working Major Cutting-edge Angle is that entire part of the cutting edge which commences at the point where the working cutting edge is zero.
Working Minor Cutting Edge - (Measured in Radian) - Working Minor Cutting Edge is the remainder of the cutting edge, where present, commences at the point on the cutting edge where is zero.

STEP 1: Convert Input(s) to Base Unit

Feed: 0.9 Millimeter --> 0.0009 Meter (Check conversion here)
Working Major Cutting-Edge Angle: 45 Degree --> 0.785398163397301 Radian (Check conversion here)
Working Minor Cutting Edge: 4.69 Degree --> 0.0818559419185187 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

R_a = f/(4*(cot(K_re)+cot(K_re'))) --> 0.0009/(4*(cot(0.785398163397301)+cot(0.0818559419185187)))

Evaluating ... ...

R_a = 1.70593002250219E-05

STEP 3: Convert Result to Output's Unit

1.70593002250219E-05 Meter -->0.0170593002250219 Millimeter (Check conversion here)

FINAL ANSWER

0.0170593002250219 ≈ 0.017059 Millimeter <-- Roughness Value

(Calculation completed in 00.004 seconds)

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Home » Engineering » Production Engineering » Metal Machining » Metal Machining Dynamics » Cutting Force and Surface Roughness » Roughness Value

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Created by Parul Keshav

National Institute of Technology (NIT), Srinagar

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Verified by Anshika Arya

National Institute Of Technology (NIT), Hamirpur

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< 21 Cutting Force and Surface Roughness Calculators

Frictional Force required to continuously shear junction between surfaces

Go Force of Friction = Real Area of Contact*((Proportion of Area of Metallic Contact*Shear Strength of Softer Metal)+((1-Proportion of Area of Metallic Contact)*Shear Strength of Softer Lubricant Layer))

Shear Strength of Softer Lubricant layer given Frictional force

Go Shear Strength of Softer Lubricant Layer = ((Force of Friction/Real Area of Contact)-(Proportion of Area of Metallic Contact*Shear Strength of Softer Metal))/(1-Proportion of Area of Metallic Contact)

Area of contact given Frictional Force

Go Real Area of Contact = Force of Friction/((Proportion of Area of Metallic Contact*Shear Strength of Softer Metal)+((1-Proportion of Area of Metallic Contact)*Shear Strength of Softer Lubricant Layer))

Proportion of Area in which metallic contact occurs given Frictional Force

Go Proportion of Area of Metallic Contact = ((Force of Friction/Real Area of Contact)-Shear Strength of Softer Lubricant Layer)/(Shear Strength of Softer Metal-Shear Strength of Softer Lubricant Layer)

Shear Strength of Softer Metal given Frictional force

Go Shear Strength of Softer Metal = ((Force of Friction/Real Area of Contact)-(1-Proportion of Area of Metallic Contact)*Shear Strength of Softer Lubricant Layer)/Proportion of Area of Metallic Contact

Working major cutting edge Angle given Roughness value

Go Working Major Cutting-Edge Angle = (acot((Feed/(4*Roughness Value))-cot(Working Minor Cutting Edge)))

Working minor cutting edge Angle given Roughness value

Go Working Minor Cutting Edge = (acot((Feed/(4*Roughness Value))-cot(Working Major Cutting-Edge Angle)))

Roughness Value

Go Roughness Value = Feed/(4*(cot(Working Major Cutting-Edge Angle)+cot(Working Minor Cutting Edge)))

Feed given Roughness value

Go Feed = 4*(cot(Working Major Cutting-Edge Angle)+cot(Working Minor Cutting Edge))*Roughness Value

Rotational Frequency of Cutter given Roughness Value

Go Rotational Frequency of Cutter = sqrt(0.0642/(Roughness Value*Diameter of Cutter))*Feed Speed

Feed speed given Roughness value

Go Feed Speed = sqrt(Roughness Value*Diameter of Cutter/0.0642)*Rotational Frequency of Cutter

Diameter of Cutter given Roughness Value

Go Diameter of Cutter = (0.0642*(Feed Speed)^2)/(Roughness Value*(Rotational Frequency of Cutter)^2)

Roughness value given feed speed

Go Roughness Value = (0.0642*(Feed Speed)^2)/(Diameter of Cutter*(Rotational Frequency of Cutter)^2)

Cutting Force given Specific Cutting Energy in Machining

Go Cutting Force = Specific Cutting Energy in Machining*Cross-sectional Area of Uncut Chip

Cutting Force given Rate of Energy Consumption during Machining

Go Cutting Force = Rate of Energy Consumption during Machining/Cutting Speed

Resultant Cutting Force using Force required to remove Chip

Go Resultant Cutting Force = Force Required to Remove Chip+Plowing Force

Force required to remove Chip and acting on Tool Face

Go Force Required to Remove Chip = Resultant Cutting Force-Plowing Force

Feed given Roughness Value and corner radius

Go Feed = (Roughness Value*Corner Radius of Tool/0.0321)^(1/2)

Roughness value given corner radius

Go Roughness Value = 0.0321*(Feed)^2/Corner Radius of Tool

Corner Radius given Roughness value

Go Corner Radius of Tool = 0.0321*(Feed)^2/Roughness Value

Roughness value of tool

Go Roughness Value = 0.0321*(Feed)^2/Corner Radius of Tool

Roughness Value Formula

Roughness Value = Feed/(4*(cot(Working Major Cutting-Edge Angle)+cot(Working Minor Cutting Edge)))
R_a = f/(4*(cot(K_re)+cot(K_re')))

what is mean roughness?

The Mean Roughness (Roughness Average Ra) is the arithmetic average of the absolute values of the roughness profile ordinates. Ra is one of the most effective surface roughness measures commonly adopted in general engineering practice. It gives a good general description of the height variations in the surface.

How to Calculate Roughness Value?

Roughness Value calculator uses Roughness Value = Feed/(4*(cot(Working Major Cutting-Edge Angle)+cot(Working Minor Cutting Edge))) to calculate 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_a symbol.

How to calculate Roughness Value using this online calculator? To use this online calculator for Roughness Value, enter Feed (f), Working Major Cutting-Edge Angle (K_re) & Working Minor Cutting Edge (K_re') and hit the calculate button. Here is how the Roughness Value calculation can be explained with given input values -> 17.0593 = 0.0009/(4*(cot(0.785398163397301)+cot(0.0818559419185187))).

FAQ

What is Roughness Value?

The Roughness Value is the arithmetic average of the absolute values of the roughness profile ordinates and is represented as R_a = f/(4*(cot(K_re)+cot(K_re'))) or Roughness Value = Feed/(4*(cot(Working Major Cutting-Edge Angle)+cot(Working Minor Cutting Edge))). The Feed is the distance the cutting tool advances along the length of the work for every revolution of the spindle, The Working Major Cutting-edge Angle is that entire part of the cutting edge which commences at the point where the working cutting edge is zero & Working Minor Cutting Edge is the remainder of the cutting edge, where present, commences at the point on the cutting edge where is zero.

How to calculate Roughness Value?

The Roughness Value is the arithmetic average of the absolute values of the roughness profile ordinates is calculated using Roughness Value = Feed/(4*(cot(Working Major Cutting-Edge Angle)+cot(Working Minor Cutting Edge))). To calculate Roughness Value, you need Feed (f), Working Major Cutting-Edge Angle (K_re) & Working Minor Cutting Edge (K_re'). With our tool, you need to enter the respective value for Feed, Working Major Cutting-Edge Angle & Working Minor Cutting Edge 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 Roughness Value?

In this formula, Roughness Value uses Feed, Working Major Cutting-Edge Angle & Working Minor Cutting Edge. We can use 3 other way(s) to calculate the same, which is/are as follows -

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

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