Rotational Frequency of Cutter given Roughness Value Calculator

✖Roughness Value is the arithmetic average of the absolute values of the roughness profile ordinates.ⓘ Roughness Value [R_a]			+10% -10%
✖The Diameter of Cutter is defined as the actual diameter of the cutter being used.ⓘ Diameter of Cutter [d_t]			+10% -10%
✖Feed Speed is the Feed given against a workpiece per unit time.ⓘ Feed Speed [V_f]			+10% -10%

✖The Rotational Frequency of Cutter known as radial or circular frequency measures angular displacement per unit time.ⓘ Rotational Frequency of Cutter given Roughness Value [n_t]

⎘ Copy

👎

Formula

✖

Rotational Frequency of Cutter given Roughness Value

Formula

`"n"_{"t"} = sqrt(0.0642/("R"_{"a"}*"d"_{"t"}))*"V"_{"f"}`

Example

`"29.99859Hz"=sqrt(0.0642/("0.017067mm"*"41.8mm"))*"100mm/s"`

Calculator

LaTeX

Reset

👍

Download Production Engineering Formula PDF

Rotational Frequency of Cutter given Roughness Value Solution

STEP 0: Pre-Calculation Summary

Formula Used

Rotational Frequency of Cutter = sqrt(0.0642/(Roughness Value*Diameter of Cutter))*Feed Speed
n_t = sqrt(0.0642/(R_a*d_t))*V_f
This formula uses 1 Functions, 4 Variables

Functions Used

sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)

Variables Used

Rotational Frequency of Cutter - (Measured in Hertz) - The Rotational Frequency of Cutter known as radial or circular frequency measures angular displacement per unit time.
Roughness Value - (Measured in Meter) - Roughness Value is the arithmetic average of the absolute values of the roughness profile ordinates.
Diameter of Cutter - (Measured in Meter) - The Diameter of Cutter is defined as the actual diameter of the cutter being used.
Feed Speed - (Measured in Meter per Second) - Feed Speed is the Feed given against a workpiece per unit time.

STEP 1: Convert Input(s) to Base Unit

Roughness Value: 0.017067 Millimeter --> 1.7067E-05 Meter (Check conversion here)
Diameter of Cutter: 41.8 Millimeter --> 0.0418 Meter (Check conversion here)
Feed Speed: 100 Millimeter per Second --> 0.1 Meter per Second (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

n_t = sqrt(0.0642/(R_a*d_t))*V_f --> sqrt(0.0642/(1.7067E-05*0.0418))*0.1

Evaluating ... ...

n_t = 29.9985856140494

STEP 3: Convert Result to Output's Unit

29.9985856140494 Hertz --> No Conversion Required

FINAL ANSWER

29.9985856140494 ≈ 29.99859 Hertz <-- Rotational Frequency of Cutter

(Calculation completed in 00.007 seconds)

You are here -

Home » Engineering » Production Engineering » Metal Machining » Metal Machining Dynamics » Cutting Force and Surface Roughness » Rotational Frequency of Cutter given Roughness Value

Credits

Created by Parul Keshav

National Institute of Technology (NIT), Srinagar

Parul Keshav has created this Calculator and 300+ more calculators!

Verified by Kumar Siddhant

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

Kumar Siddhant has verified this Calculator and 100+ more calculators!

< 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

Rotational Frequency of Cutter given Roughness Value Formula

Rotational Frequency of Cutter = sqrt(0.0642/(Roughness Value*Diameter of Cutter))*Feed Speed
n_t = sqrt(0.0642/(R_a*d_t))*V_f

How roughness is measured?

With a contact-type roughness meter, surface roughness is measured by tracing the probe across the surface of the target. In contrast, a laser-based non-contact roughness meter emits a laser beam onto the target and detects the reflected light to measure the roughness.

How to Calculate Rotational Frequency of Cutter given Roughness Value?

Rotational Frequency of Cutter given Roughness Value calculator uses Rotational Frequency of Cutter = sqrt(0.0642/(Roughness Value*Diameter of Cutter))*Feed Speed to calculate the Rotational Frequency of Cutter, Rotational Frequency of Cutter given Roughness Value formula measures angular displacement of the cutter per unit time, also known as radial or circular frequency. Rotational Frequency of Cutter is denoted by n_t symbol.

How to calculate Rotational Frequency of Cutter given Roughness Value using this online calculator? To use this online calculator for Rotational Frequency of Cutter given Roughness Value, enter Roughness Value (R_a), Diameter of Cutter (d_t) & Feed Speed (V_f) and hit the calculate button. Here is how the Rotational Frequency of Cutter given Roughness Value calculation can be explained with given input values -> 29.99859 = sqrt(0.0642/(1.7067E-05*0.0418))*0.1.

FAQ

What is Rotational Frequency of Cutter given Roughness Value?

Rotational Frequency of Cutter given Roughness Value formula measures angular displacement of the cutter per unit time, also known as radial or circular frequency and is represented as n_t = sqrt(0.0642/(R_a*d_t))*V_f or Rotational Frequency of Cutter = sqrt(0.0642/(Roughness Value*Diameter of Cutter))*Feed Speed. Roughness Value is the arithmetic average of the absolute values of the roughness profile ordinates, The Diameter of Cutter is defined as the actual diameter of the cutter being used & Feed Speed is the Feed given against a workpiece per unit time.

How to calculate Rotational Frequency of Cutter given Roughness Value?

Rotational Frequency of Cutter given Roughness Value formula measures angular displacement of the cutter per unit time, also known as radial or circular frequency is calculated using Rotational Frequency of Cutter = sqrt(0.0642/(Roughness Value*Diameter of Cutter))*Feed Speed. To calculate Rotational Frequency of Cutter given Roughness Value, you need Roughness Value (R_a), Diameter of Cutter (d_t) & Feed Speed (V_f). With our tool, you need to enter the respective value for Roughness Value, Diameter of Cutter & Feed Speed and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

Home

FREE PDFs

🔍 Search