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Side cutting edge angle for given width of cut Formula

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Side cutting edge angle for metal cutting can be defined as the angle between the side cutting edge and the side of the tool shank. Check FAQs

ψ = a \cos (\frac{d cut}{w c})

ψ - Side Cutting Edge Angle for Metal Cutting?d_cut - Depth of Cut Provided by Tool?w_c - Cutting Width?

Side cutting edge angle for given width of cut Example

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Here is how the Side cutting edge angle for given width of cut equation looks like with Values.

Here is how the Side cutting edge angle for given width of cut equation looks like with Units.

Here is how the Side cutting edge angle for given width of cut equation looks like.

20.5105 = a \cos (\frac{9.0732}{9.6873})

20.5105° = a \cos (\frac{9.0732mm}{9.6873mm})

20.5105 = a \cos (\frac{9.0732}{9.6873})

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Side cutting edge angle for given width of cut Solution

Follow our step by step solution on how to calculate Side cutting edge angle for given width of cut?

FIRST Step Consider the formula

ψ = a \cos (\frac{d cut}{w c})

Next Step Substitute values of Variables

∴

ψ = a \cos (\frac{9.0732mm}{9.6873mm})

Next Step Convert Units

∴

ψ = a \cos (\frac{0.0091m}{0.0097m})

Next Step Prepare to Evaluate

∴

ψ = a \cos (\frac{0.0091}{0.0097})

Next Step Evaluate

∴

ψ = 0.357976530109204rad

Next Step Convert to Output's Unit

∴

ψ = 20.5105443399991°

LAST Step Rounding Answer

∴

ψ = 20.5105°

Side cutting edge angle for given width of cut Formula Elements

Variables

Functions

Side Cutting Edge Angle for Metal Cutting

Side cutting edge angle for metal cutting can be defined as the angle between the side cutting edge and the side of the tool shank.

Symbol: ψ

Measurement: AngleUnit: °

Note: Value should be greater than 0.

Formulas to find Side Cutting Edge Angle for Metal Cutting

Depth of Cut Provided by Tool

Depth of cut provided by tool provides necessary depth to workpiece that is required to remove material during machining process.

Symbol: d_cut

Measurement: LengthUnit: mm

Note: Value can be positive or negative.

Formulas to find Depth of Cut Provided by Tool

Cutting Width

Cutting Width can be defined as the width the tool cuts into the workpiece.

Symbol: w_c

Measurement: LengthUnit: mm

Note: Value can be positive or negative.

Formulas to find Cutting Width

cos

Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle.

Syntax: cos(Angle)

acos

The inverse cosine function, is the inverse function of the cosine function. It is the function that takes a ratio as an input and returns the angle whose cosine is equal to that ratio.

Syntax: acos(Number)

Other formulas in Geometry and Dimensions category

Go Area of shear plane for given shear angle, width of cut and uncut chip thickness

A s = \frac{t 1 \cdot w c}{\sin (ϕ)}

Go Shear angle for given area of shear plane, width of cut and uncut chip thickness

ϕ = a \sin (w c \cdot \frac{t 1}{A s})

Go Uncut chip thickness for given width of cut, shear angle and area of shear plane

t 1 = \frac{A s \cdot \sin (ϕ)}{w c}

Go Width of cut for given shear angle, uncut chip thickness and area of shear plane

w c = \frac{A s \cdot \sin (ϕ)}{t 1}

How to Evaluate Side cutting edge angle for given width of cut?

Side cutting edge angle for given width of cut evaluator uses Side Cutting Edge Angle for Metal Cutting = acos(Depth of Cut Provided by Tool/Cutting Width) to evaluate the Side Cutting Edge Angle for Metal Cutting, The Side cutting edge angle for given width of cut formula is defined as cos inverse of the ratio of the width of cut to the depth of cut. Side Cutting Edge Angle for Metal Cutting is denoted by ψ symbol.

How to evaluate Side cutting edge angle for given width of cut using this online evaluator? To use this online evaluator for Side cutting edge angle for given width of cut, enter Depth of Cut Provided by Tool (d_cut) & Cutting Width (w_c) and hit the calculate button.

FAQs on Side cutting edge angle for given width of cut

What is the formula to find Side cutting edge angle for given width of cut?

The formula of Side cutting edge angle for given width of cut is expressed as Side Cutting Edge Angle for Metal Cutting = acos(Depth of Cut Provided by Tool/Cutting Width). Here is an example- 1175.168 = acos(0.0090732/0.0096873).

How to calculate Side cutting edge angle for given width of cut?

With Depth of Cut Provided by Tool (d_cut) & Cutting Width (w_c) we can find Side cutting edge angle for given width of cut using the formula - Side Cutting Edge Angle for Metal Cutting = acos(Depth of Cut Provided by Tool/Cutting Width). This formula also uses Cosine (cos), Inverse Cosine (acos) function(s).

Can the Side cutting edge angle for given width of cut be negative?

No, the Side cutting edge angle for given width of cut, measured in Angle cannot be negative.

Which unit is used to measure Side cutting edge angle for given width of cut?

Side cutting edge angle for given width of cut is usually measured using the Degree[°] for Angle. Radian[°], Minute[°], Second[°] are the few other units in which Side cutting edge angle for given width of cut can be measured.

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