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Diameter of Cutter given Roughness Value Formula

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The Diameter of Cutter is defined as the actual diameter of the cutter being used. Check FAQs

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

d_t - Diameter of Cutter?V_f - Feed Speed?R - Roughness Value?ω_c - Rotational Frequency of Cutter?

Diameter of Cutter given Roughness Value Example

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With units

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Here is how the Diameter of Cutter given Roughness Value equation looks like with Values.

Here is how the Diameter of Cutter given Roughness Value equation looks like with Units.

Here is how the Diameter of Cutter given Roughness Value equation looks like.

41.7961 = \frac{0.0642 \cdot {(100)}^{2}}{0.0171 \cdot {(30)}^{2}}

41.7961mm = \frac{0.0642 \cdot {(100mm/s)}^{2}}{0.0171mm \cdot {(30Hz)}^{2}}

41.7961 = \frac{0.0642 \cdot {(100)}^{2}}{0.0171 \cdot {(30)}^{2}}

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Diameter of Cutter given Roughness Value Solution

Follow our step by step solution on how to calculate Diameter of Cutter given Roughness Value?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

d t = \frac{0.0642 \cdot {(100mm/s)}^{2}}{0.0171mm \cdot {(30Hz)}^{2}}

Next Step Convert Units

∴

d t = \frac{0.0642 \cdot {(0.1m/s)}^{2}}{1.7E-5m \cdot {(30Hz)}^{2}}

Next Step Prepare to Evaluate

∴

d t = \frac{0.0642 \cdot {(0.1)}^{2}}{1.7E-5 \cdot {(30)}^{2}}

Next Step Evaluate

∴

d t = 0.0417960586707291m

Next Step Convert to Output's Unit

∴

d t = 41.7960586707291mm

LAST Step Rounding Answer

∴

d t = 41.7961mm

Diameter of Cutter given Roughness Value Formula Elements

Variables

Diameter of Cutter

The Diameter of Cutter is defined as the actual diameter of the cutter being used.

Symbol: d_t

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Diameter of Cutter

Feed Speed

Feed Speed is the feed given against a workpiece per unit time.

Symbol: V_f

Measurement: SpeedUnit: mm/s

Note: Value should be greater than 0.

Formulas to find Feed Speed

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

Rotational Frequency of Cutter

Rotational Frequency of Cutter known as radial or circular frequency measures angular displacement per unit time.

Symbol: ω_c

Measurement: FrequencyUnit: Hz

Note: Value should be greater than 0.

Formulas to find Rotational Frequency of Cutter

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 Diameter of Cutter given Roughness Value?

Diameter of Cutter given Roughness Value evaluator uses Diameter of Cutter = (0.0642*(Feed Speed)^2)/(Roughness Value*(Rotational Frequency of Cutter)^2) to evaluate 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 evaluate Diameter of Cutter given Roughness Value using this online evaluator? To use this online evaluator for Diameter of Cutter given Roughness Value, enter Feed Speed (V_f), Roughness Value (R) & Rotational Frequency of Cutter (ω_c) and hit the calculate button.

FAQs on Diameter of Cutter given Roughness Value

What is the formula to find Diameter of Cutter given Roughness Value?

The formula of Diameter of Cutter given Roughness Value is expressed as Diameter of Cutter = (0.0642*(Feed Speed)^2)/(Roughness Value*(Rotational Frequency of Cutter)^2). Here is an example- 41796.06 = (0.0642*(0.1)^2)/(1.7067E-05*(30)^2).

How to calculate Diameter of Cutter given Roughness Value?

With Feed Speed (V_f), Roughness Value (R) & Rotational Frequency of Cutter (ω_c) we can find Diameter of Cutter given Roughness Value using the formula - Diameter of Cutter = (0.0642*(Feed Speed)^2)/(Roughness Value*(Rotational Frequency of Cutter)^2).

Can the Diameter of Cutter given Roughness Value be negative?

No, the Diameter of Cutter given Roughness Value, measured in Length cannot be negative.

Which unit is used to measure Diameter of Cutter given Roughness Value?

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

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Diameter of Cutter given Roughness Value Formula

Diameter of Cutter given Roughness Value Example

Diameter of Cutter given Roughness Value Solution

Diameter of Cutter given Roughness Value Formula Elements

Other formulas in Cutting Force and Surface Roughness category

How to Evaluate Diameter of Cutter given Roughness Value?

FAQs on Diameter of Cutter given Roughness Value

Variable Name