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Back Rake Angle Formula

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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. Check FAQs

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

α_b - Back Rake Angle?λ - Approach or Entering Angle?α - Orthogonal Rake Angle?𝒊 - Inclination Angle?

Back Rake Angle Example

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With units

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

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

Here is how the Back Rake Angle equation looks like.

36.3871 = a \tan ((\cos (15) \cdot \tan (37)) + (\sin (15) \cdot \tan (2)))

36.3871° = a \tan ((\cos (15°) \cdot \tan (37°)) + (\sin (15°) \cdot \tan (2°)))

36.3871 = a \tan ((\cos (15) \cdot \tan (37)) + (\sin (15) \cdot \tan (2)))

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Back Rake Angle Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

α b = a \tan ((\cos (15°) \cdot \tan (37°)) + (\sin (15°) \cdot \tan (2°)))

Next Step Convert Units

∴

α b = a \tan ((\cos (0.2618rad) \cdot \tan (0.6458rad)) + (\sin (0.2618rad) \cdot \tan (0.0349rad)))

Next Step Prepare to Evaluate

∴

α b = a \tan ((\cos (0.2618) \cdot \tan (0.6458)) + (\sin (0.2618) \cdot \tan (0.0349)))

Next Step Evaluate

∴

α b = 0.635074288150182rad

Next Step Convert to Output's Unit

∴

α b = 36.3870763882874°

LAST Step Rounding Answer

∴

α b = 36.3871°

Back Rake Angle Formula Elements

Variables

Functions

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

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 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 Back Rake Angle?

Back Rake Angle evaluator uses Back Rake Angle = atan((cos(Approach or Entering Angle)*tan(Orthogonal Rake Angle))+(sin(Approach or Entering Angle)*tan(Inclination Angle))) to evaluate the Back Rake Angle, The Back Rake Angle is the inclination of the face toward or away from the end or the end cutting edge of the tool. Back Rake Angle is denoted by α_b symbol.

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

FAQs on Back Rake Angle

What is the formula to find Back Rake Angle?

The formula of Back Rake Angle is expressed as Back Rake Angle = atan((cos(Approach or Entering Angle)*tan(Orthogonal Rake Angle))+(sin(Approach or Entering Angle)*tan(Inclination Angle))). Here is an example- 3310.218 = atan((cos(0.2617993877991)*tan(0.64577182323778))+(sin(0.2617993877991)*tan(0.03490658503988))).

How to calculate Back Rake Angle?

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

Can the Back Rake Angle be negative?

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

Which unit is used to measure Back Rake Angle?

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

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Back Rake Angle Formula

Back Rake Angle Example

Back Rake Angle Solution

Back Rake Angle Formula Elements

Other formulas in Metal Cutting Tools category

How to Evaluate Back Rake Angle?

FAQs on Back Rake Angle

Variable Name