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Side Rake Angle Formula

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The Side Rake Angle of Tool is an angle between the tool face and a line parallel to the base of the tool and measured in a plane perpendicular to the base at the side cutting edge. Check FAQs

α sr = a \tan ((\sin (λ) \cdot \tan (α)) - (\cos (λ) \cdot \tan (𝒊)))

α_sr - Side Rake Angle of Tool?λ - Approach or Entering Angle?α - Orthogonal Rake Angle?𝒊 - Inclination Angle?

Side Rake Angle Example

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Here is how the Side Rake Angle equation looks like with Values.

Here is how the Side Rake Angle equation looks like with Units.

Here is how the Side Rake Angle equation looks like.

9.1631 = a \tan ((\sin (15) \cdot \tan (37)) - (\cos (15) \cdot \tan (2)))

9.1631° = a \tan ((\sin (15°) \cdot \tan (37°)) - (\cos (15°) \cdot \tan (2°)))

9.1631 = a \tan ((\sin (15) \cdot \tan (37)) - (\cos (15) \cdot \tan (2)))

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Side Rake Angle Solution

Follow our step by step solution on how to calculate Side Rake Angle?

FIRST Step Consider the formula

α sr = a \tan ((\sin (λ) \cdot \tan (α)) - (\cos (λ) \cdot \tan (𝒊)))

Next Step Substitute values of Variables

∴

α sr = a \tan ((\sin (15°) \cdot \tan (37°)) - (\cos (15°) \cdot \tan (2°)))

Next Step Convert Units

∴

α sr = a \tan ((\sin (0.2618rad) \cdot \tan (0.6458rad)) - (\cos (0.2618rad) \cdot \tan (0.0349rad)))

Next Step Prepare to Evaluate

∴

α sr = a \tan ((\sin (0.2618) \cdot \tan (0.6458)) - (\cos (0.2618) \cdot \tan (0.0349)))

Next Step Evaluate

∴

α sr = 0.159925738912531rad

Next Step Convert to Output's Unit

∴

α sr = 9.16306987520086°

LAST Step Rounding Answer

∴

α sr = 9.1631°

Side Rake Angle Formula Elements

Variables

Functions

Side Rake Angle of Tool

The Side Rake Angle of Tool is an angle between the tool face and a line parallel to the base of the tool and measured in a plane perpendicular to the base at the side cutting edge.

Symbol: α_sr

Measurement: AngleUnit: °

Note: Value should be greater than 0.

Formulas to find Side Rake Angle of Tool

Approach or Entering Angle

The Approach or Entering Angle is the angle between a plane perpendicular to the cutter axis and a plane tangent to the surface of the revolution of the cutting edges.

Symbol: λ

Measurement: AngleUnit: °

Note: Value can be positive or negative.

Formulas to find Approach or Entering Angle

Orthogonal Rake Angle

Orthogonal Rake Angle is the angle of orientation of the tool’s rake surface from the reference plane and measured on the orthogonal plane.

Symbol: α

Measurement: AngleUnit: °

Note: Value can be positive or negative.

Formulas to find Orthogonal Rake Angle

Inclination Angle

Inclination Angle is the angle of inclination of the tool’s principal cutting edge from the reference plane and measured on the cutting plane.

Symbol: 𝒊

Measurement: AngleUnit: °

Note: Value can be positive or negative.

Formulas to find Inclination Angle

sin

Sine is a trigonometric function that describes the ratio of the length of the opposite side of a right triangle to the length of the hypotenuse.

Syntax: sin(Angle)

cos

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

Syntax: cos(Angle)

tan

The tangent of an angle is a trigonometric ratio of the length of the side opposite an angle to the length of the side adjacent to an angle in a right triangle.

Syntax: tan(Angle)

atan

Inverse tan is used to calculate the angle by applying the tangent ratio of the angle, which is the opposite side divided by the adjacent side of the right triangle.

Syntax: atan(Number)

Other formulas in Metal Cutting Tools category

Go Orthogonal Rake Angle

α = \arctan ((\tan (α sr) \cdot \sin (λ)) + (\tan (α b) \cdot \cos (λ)))

Go Back Rake Angle

α b = a \tan ((\cos (λ) \cdot \tan (α)) + (\sin (λ) \cdot \tan (𝒊)))

Go Inclination Angle

𝒊 = a \tan ((\tan (α b) \cdot \sin (λ)) - (\tan (α sr) \cdot \cos (λ)))

Go Lead (approach or entering) angle for given side cutting edge angle

λ = 1.5708 - ψ

How to Evaluate Side Rake Angle?

Side Rake Angle evaluator uses Side Rake Angle of Tool = atan((sin(Approach or Entering Angle)*tan(Orthogonal Rake Angle))-(cos(Approach or Entering Angle)*tan(Inclination Angle))) to evaluate the Side Rake Angle of Tool, The Side Rake Angle is defined as the inclination of the face toward or away from the side cutting edge. Side Rake Angle of Tool is denoted by α_sr symbol.

How to evaluate Side Rake Angle using this online evaluator? To use this online evaluator for Side Rake Angle, enter Approach or Entering Angle (λ), Orthogonal Rake Angle (α) & Inclination Angle (𝒊) and hit the calculate button.

FAQs on Side Rake Angle

What is the formula to find Side Rake Angle?

The formula of Side Rake Angle is expressed as Side Rake Angle of Tool = atan((sin(Approach or Entering Angle)*tan(Orthogonal Rake Angle))-(cos(Approach or Entering Angle)*tan(Inclination Angle))). Here is an example- 525.0052 = atan((sin(0.2617993877991)*tan(0.64577182323778))-(cos(0.2617993877991)*tan(0.03490658503988))).

How to calculate Side Rake Angle?

With Approach or Entering Angle (λ), Orthogonal Rake Angle (α) & Inclination Angle (𝒊) we can find Side Rake Angle using the formula - Side Rake Angle of Tool = atan((sin(Approach or Entering Angle)*tan(Orthogonal Rake Angle))-(cos(Approach or Entering Angle)*tan(Inclination Angle))). This formula also uses Sine (sin)Cosine (cos)Tangent (tan), Inverse Tan (atan) function(s).

Can the Side Rake Angle be negative?

No, the Side Rake Angle, measured in Angle cannot be negative.

Which unit is used to measure Side Rake Angle?

Side Rake Angle is usually measured using the Degree[°] for Angle. Radian[°], Minute[°], Second[°] are the few other units in which Side Rake Angle can be measured.

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Side Rake Angle Formula

Side Rake Angle Example

Side Rake Angle Solution

Side Rake Angle Formula Elements

Other formulas in Metal Cutting Tools category

How to Evaluate Side Rake Angle?

FAQs on Side Rake Angle

Variable Name