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Inclination Angle Formula

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

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

𝒊 - Inclination Angle?α_b - Back Rake Angle?λ - Approach or Entering Angle?α_sr - Side Rake Angle of Tool?

Inclination Angle Example

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Here is how the Inclination Angle equation looks like with Values.

Here is how the Inclination Angle equation looks like with Units.

Here is how the Inclination Angle equation looks like.

2 = a \tan ((\tan (36.3871) \cdot \sin (15)) - (\tan (9.1631) \cdot \cos (15)))

2° = a \tan ((\tan (36.3871°) \cdot \sin (15°)) - (\tan (9.1631°) \cdot \cos (15°)))

2 = a \tan ((\tan (36.3871) \cdot \sin (15)) - (\tan (9.1631) \cdot \cos (15)))

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Inclination Angle Solution

Follow our step by step solution on how to calculate Inclination Angle?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

𝒊 = a \tan ((\tan (36.3871°) \cdot \sin (15°)) - (\tan (9.1631°) \cdot \cos (15°)))

Next Step Convert Units

∴

𝒊 = a \tan ((\tan (0.6351rad) \cdot \sin (0.2618rad)) - (\tan (0.1599rad) \cdot \cos (0.2618rad)))

Next Step Prepare to Evaluate

∴

𝒊 = a \tan ((\tan (0.6351) \cdot \sin (0.2618)) - (\tan (0.1599) \cdot \cos (0.2618)))

Next Step Evaluate

∴

𝒊 = 0.0349062289795786rad

Next Step Convert to Output's Unit

∴

𝒊 = 1.99997959924748°

LAST Step Rounding Answer

∴

𝒊 = 2°

Inclination Angle Formula Elements

Variables

Functions

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

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

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

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 Side Rake Angle

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

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

λ = 1.5708 - ψ

How to Evaluate Inclination Angle?

Inclination Angle evaluator uses Inclination Angle = atan((tan(Back Rake Angle)*sin(Approach or Entering Angle))-(tan(Side Rake Angle of Tool)*cos(Approach or Entering Angle))) to evaluate the Inclination Angle, The Inclination Angle is defined as the angle of inclination of the tool’s principal cutting edge from the reference plane and measured on the cutting plane. Inclination Angle is denoted by 𝒊 symbol.

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

FAQs on Inclination Angle

What is the formula to find Inclination Angle?

The formula of Inclination Angle is expressed as Inclination Angle = atan((tan(Back Rake Angle)*sin(Approach or Entering Angle))-(tan(Side Rake Angle of Tool)*cos(Approach or Entering Angle))). Here is an example- -1154.543898 = atan((tan(0.635074700252309)*sin(0.2617993877991))-(tan(0.159926264689462)*cos(0.2617993877991))).

How to calculate Inclination Angle?

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

Can the Inclination Angle be negative?

Yes, the Inclination Angle, measured in Angle can be negative.

Which unit is used to measure Inclination Angle?

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

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Inclination Angle Formula

Inclination Angle Example

Inclination Angle Solution

Inclination Angle Formula Elements

Other formulas in Metal Cutting Tools category

How to Evaluate Inclination Angle?

FAQs on Inclination Angle

Variable Name