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Working Major Cutting Edge Angle given Roughness Value Formula

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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. Check FAQs

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

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

Working Major Cutting Edge Angle given Roughness Value Example

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Here is how the Working Major Cutting Edge Angle given Roughness Value equation looks like with Values.

Here is how the Working Major Cutting Edge Angle given Roughness Value equation looks like with Units.

Here is how the Working Major Cutting Edge Angle given Roughness Value equation looks like.

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

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

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

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Working Major Cutting Edge Angle given Roughness Value Solution

Follow our step by step solution on how to calculate Working Major Cutting Edge Angle given Roughness Value?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

θ = (a \cot ((\frac{0.9mm}{4 \cdot 0.0171mm}) - \cot (4.69°)))

Next Step Convert Units

∴

θ = (a \cot ((\frac{0.0009m}{4 \cdot 1.7E-5m}) - \cot (0.0819rad)))

Next Step Prepare to Evaluate

∴

θ = (a \cot ((\frac{0.0009}{4 \cdot 1.7E-5}) - \cot (0.0819)))

Next Step Evaluate

∴

θ = 0.788382205131509rad

Next Step Convert to Output's Unit

∴

θ = 45.1709729972611°

LAST Step Rounding Answer

∴

θ = 45.171°

Working Major Cutting Edge Angle given Roughness Value Formula Elements

Variables

Functions

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

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

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

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)

acot

The ACOT function calculates the arccotangent of a given number which is an angle given in radians from 0 (zero) to pi.

Syntax: acot(Number)

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 Working Major Cutting Edge Angle given Roughness Value?

Working Major Cutting Edge Angle given Roughness Value evaluator uses Working Major Cutting Edge Angle = (acot((Feed/(4*Roughness Value))-cot(Working Minor Cutting Edge))) to evaluate the Working Major Cutting Edge Angle, Working Major Cutting Edge Angle given Roughness Value is that the entire part of the cutting edge which commences at the point where the working cutting edge angle is zero and of which at least a portion produces the transient surface on the workpiece. Working Major Cutting Edge Angle is denoted by θ symbol.

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

FAQs on Working Major Cutting Edge Angle given Roughness Value

What is the formula to find Working Major Cutting Edge Angle given Roughness Value?

The formula of Working Major Cutting Edge Angle given Roughness Value is expressed as Working Major Cutting Edge Angle = (acot((Feed/(4*Roughness Value))-cot(Working Minor Cutting Edge))). Here is an example- 2588.106 = (acot((0.0009/(4*1.7067E-05))-cot(0.0818559419185187))).

How to calculate Working Major Cutting Edge Angle given Roughness Value?

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

Can the Working Major Cutting Edge Angle given Roughness Value be negative?

No, the Working Major Cutting Edge Angle given Roughness Value, measured in Angle cannot be negative.

Which unit is used to measure Working Major Cutting Edge Angle given Roughness Value?

Working Major Cutting Edge Angle given Roughness Value is usually measured using the Degree[°] for Angle. Radian[°], Minute[°], Second[°] are the few other units in which Working Major Cutting Edge Angle given Roughness Value can be measured.

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Working Major Cutting Edge Angle given Roughness Value Formula

Working Major Cutting Edge Angle given Roughness Value Example

Working Major Cutting Edge Angle given Roughness Value Solution

Working Major Cutting Edge Angle given Roughness Value Formula Elements

Other formulas in Cutting Force and Surface Roughness category

How to Evaluate Working Major Cutting Edge Angle given Roughness Value?

FAQs on Working Major Cutting Edge Angle given Roughness Value

Variable Name