Diameter of Cutter given Roughness Value Calculator

✖Feed Speed is the Feed given against a workpiece per unit time.ⓘ Feed Speed [V_f]			+10% -10%
✖Roughness Value is the arithmetic average of the absolute values of the roughness profile ordinates.ⓘ Roughness Value [R_a]			+10% -10%
✖The Rotational Frequency of Cutter known as radial or circular frequency measures angular displacement per unit time.ⓘ Rotational Frequency of Cutter [n_t]			+10% -10%

✖The Diameter of Cutter is defined as the actual diameter of the cutter being used.ⓘ Diameter of Cutter given Roughness Value [d_t]

⎘ Copy

👎

Formula

✖

Diameter of Cutter given Roughness Value

Formula

`"d"_{"t"} = (0.0642*("V"_{"f"})^2)/("R"_{"a"}*("n"_{"t"})^2)`

Example

`"41.79606mm"=(0.0642*("100mm/s")^2)/("0.017067mm"*("30Hz")^2)`

Calculator

LaTeX

Reset

👍

Download Production Engineering Formula PDF PDF Image

Diameter of Cutter given Roughness Value Solution

STEP 0: Pre-Calculation Summary

Formula Used

Diameter of Cutter = (0.0642*(Feed Speed)^2)/(Roughness Value*(Rotational Frequency of Cutter)^2)
d_t = (0.0642*(V_f)^2)/(R_a*(n_t)^2)
This formula uses 4 Variables

Variables Used

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.
Roughness Value - (Measured in Meter) - Roughness Value is the arithmetic average of the absolute values of the roughness profile ordinates.
Rotational Frequency of Cutter - (Measured in Hertz) - The Rotational Frequency of Cutter known as radial or circular frequency measures angular displacement per unit time.

STEP 1: Convert Input(s) to Base Unit

Feed Speed: 100 Millimeter per Second --> 0.1 Meter per Second (Check conversion here)
Roughness Value: 0.017067 Millimeter --> 1.7067E-05 Meter (Check conversion here)
Rotational Frequency of Cutter: 30 Hertz --> 30 Hertz No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

d_t = (0.0642*(V_f)^2)/(R_a*(n_t)^2) --> (0.0642*(0.1)^2)/(1.7067E-05*(30)^2)

Evaluating ... ...

d_t = 0.0417960586707291

STEP 3: Convert Result to Output's Unit

0.0417960586707291 Meter -->41.7960586707291 Millimeter (Check conversion here)

FINAL ANSWER

41.7960586707291 ≈ 41.79606 Millimeter <-- Diameter of Cutter

(Calculation completed in 00.020 seconds)

You are here -

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

Diameter of Cutter given Roughness Value Formula

Diameter of Cutter = (0.0642*(Feed Speed)^2)/(Roughness Value*(Rotational Frequency of Cutter)^2)
d_t = (0.0642*(V_f)^2)/(R_a*(n_t)^2)

What is the difference between feed rate, cutting speed and depth of cut?

Cutting speed is defined as the speed at which the work moves with respect to the tool (usually measured in feet per minute). Feed rate is defined as the distance the tool travels during one revolution of the part. Cutting speed and feed determines the surface finish, power requirements, and material removal rate. The primary factor in choosing feed and speed is the material to be cut.

How to Calculate Diameter of Cutter given Roughness Value?

Diameter of Cutter given Roughness Value calculator uses Diameter of Cutter = (0.0642*(Feed Speed)^2)/(Roughness Value*(Rotational Frequency of Cutter)^2) to calculate the Diameter of Cutter, The Diameter of Cutter given Roughness Value is defined as the actual diameter of the cutter used in the metal cutting operation. Diameter of Cutter is denoted by d_t symbol.

How to calculate Diameter of Cutter given Roughness Value using this online calculator? To use this online calculator for Diameter of Cutter given Roughness Value, enter Feed Speed (V_f), Roughness Value (R_a) & Rotational Frequency of Cutter (n_t) and hit the calculate button. Here is how the Diameter of Cutter given Roughness Value calculation can be explained with given input values -> 41796.06 = (0.0642*(0.1)^2)/(1.7067E-05*(30)^2).

FAQ

What is Diameter of Cutter given Roughness Value?

The Diameter of Cutter given Roughness Value is defined as the actual diameter of the cutter used in the metal cutting operation and is represented as d_t = (0.0642*(V_f)^2)/(R_a*(n_t)^2) or Diameter of Cutter = (0.0642*(Feed Speed)^2)/(Roughness Value*(Rotational Frequency of Cutter)^2). Feed Speed is the Feed given against a workpiece per unit time, Roughness Value is the arithmetic average of the absolute values of the roughness profile ordinates & The Rotational Frequency of Cutter known as radial or circular frequency measures angular displacement per unit time.

How to calculate Diameter of Cutter given Roughness Value?

The Diameter of Cutter given Roughness Value is defined as the actual diameter of the cutter used in the metal cutting operation is calculated using Diameter of Cutter = (0.0642*(Feed Speed)^2)/(Roughness Value*(Rotational Frequency of Cutter)^2). To calculate Diameter of Cutter given Roughness Value, you need Feed Speed (V_f), Roughness Value (R_a) & Rotational Frequency of Cutter (n_t). With our tool, you need to enter the respective value for Feed Speed, Roughness Value & Rotational Frequency of Cutter 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