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Orthogonal Rake Angle Formula

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

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

α - Orthogonal Rake Angle?α_sr - Side Rake Angle of Tool?λ - Approach or Entering Angle?α_b - Back Rake Angle?

Orthogonal Rake Angle Example

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

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

Here is how the Orthogonal Rake Angle equation looks like.

37 = \arctan ((\tan (9.1631) \cdot \sin (15)) + (\tan (36.3871) \cdot \cos (15)))

37° = \arctan ((\tan (9.1631°) \cdot \sin (15°)) + (\tan (36.3871°) \cdot \cos (15°)))

37 = \arctan ((\tan (9.1631) \cdot \sin (15)) + (\tan (36.3871) \cdot \cos (15)))

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Orthogonal Rake Angle Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

α = \arctan ((\tan (9.1631°) \cdot \sin (15°)) + (\tan (36.3871°) \cdot \cos (15°)))

Next Step Convert Units

∴

α = \arctan ((\tan (0.1599rad) \cdot \sin (0.2618rad)) + (\tan (0.6351rad) \cdot \cos (0.2618rad)))

Next Step Prepare to Evaluate

∴

α = \arctan ((\tan (0.1599) \cdot \sin (0.2618)) + (\tan (0.6351) \cdot \cos (0.2618)))

Next Step Evaluate

∴

α = 0.64577230405488rad

Next Step Convert to Output's Unit

∴

α = 37.0000275487905°

LAST Step Rounding Answer

∴

α = 37°

Orthogonal Rake Angle Formula Elements

Variables

Functions

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

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

Back Rake Angle

The Back Rake Angle or Top Rake Angle is the angle between the face of the tool and a line parallel to the base of the tool and measured in a plane (perpendicular) through the side cutting edge.

Symbol: α_b

Measurement: AngleUnit: °

Note: Value should be greater than 0.

Formulas to find Back Rake 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)

ctan

Cotangent is a trigonometric function that is defined as the ratio of the adjacent side to the opposite side in a right triangle.

Syntax: ctan(Angle)

arctan

Inverse trigonometric functions are usually accompanied by the prefix - arc. Mathematically, we represent arctan or the inverse tangent function as tan-1 x or arctan(x).

Syntax: arctan(Number)

Other formulas in Metal Cutting Tools category

Go Back Rake Angle

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

Go Side Rake Angle

α sr = a \tan ((\sin (λ) \cdot \tan (α)) - (\cos (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 Orthogonal Rake Angle?

Orthogonal Rake Angle evaluator uses Orthogonal Rake Angle = arctan((tan(Side Rake Angle of Tool)*sin(Approach or Entering Angle))+(tan(Back Rake Angle)*cos(Approach or Entering Angle))) to evaluate the Orthogonal Rake Angle, Orthogonal Rake Angle is the angle of inclination of the tool’s rake surface from the reference plane and measured on the orthogonal plane. Orthogonal Rake Angle is denoted by α symbol.

How to evaluate Orthogonal Rake Angle using this online evaluator? To use this online evaluator for Orthogonal Rake Angle, enter Side Rake Angle of Tool (α_sr), Approach or Entering Angle (λ) & Back Rake Angle (α_b) and hit the calculate button.

FAQs on Orthogonal Rake Angle

What is the formula to find Orthogonal Rake Angle?

The formula of Orthogonal Rake Angle is expressed as Orthogonal Rake Angle = arctan((tan(Side Rake Angle of Tool)*sin(Approach or Entering Angle))+(tan(Back Rake Angle)*cos(Approach or Entering Angle))). Here is an example- 2334.012 = arctan((tan(0.159926264689462)*sin(0.2617993877991))+(tan(0.635074700252309)*cos(0.2617993877991))).

How to calculate Orthogonal Rake Angle?

With Side Rake Angle of Tool (α_sr), Approach or Entering Angle (λ) & Back Rake Angle (α_b) we can find Orthogonal Rake Angle using the formula - Orthogonal Rake Angle = arctan((tan(Side Rake Angle of Tool)*sin(Approach or Entering Angle))+(tan(Back Rake Angle)*cos(Approach or Entering Angle))). This formula also uses Sine (sin)Cosine (cos)Tangent (tan)Cotangent (ctan), Inverse Tangent (arctan) function(s).

Can the Orthogonal Rake Angle be negative?

Yes, the Orthogonal Rake Angle, measured in Angle can be negative.

Which unit is used to measure Orthogonal Rake Angle?

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

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Orthogonal Rake Angle Formula

Orthogonal Rake Angle Example

Orthogonal Rake Angle Solution

Orthogonal Rake Angle Formula Elements

Other formulas in Metal Cutting Tools category

How to Evaluate Orthogonal Rake Angle?

FAQs on Orthogonal Rake Angle

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