Inclination Angle Calculator

✖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.ⓘ Back Rake Angle [α_b]			+10% -10%
✖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.ⓘ Approach or Entering Angle [λ]			+10% -10%
✖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.ⓘ Side Rake Angle of Tool [α_sr]			+10% -10%

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

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Formula

✖

Inclination Angle

Formula

`"𝒊" = atan((tan("α"_{"b"})*sin("λ"))-(tan("α"_{"sr"})*cos("λ")))`

Example

`"1.99998°"=atan((tan("36.3871°")*sin("15°"))-(tan("9.1631°")*cos("15°")))`

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Inclination Angle Solution

STEP 0: Pre-Calculation Summary

Formula Used

Inclination Angle = atan((tan(Back Rake Angle)*sin(Approach or Entering Angle))-(tan(Side Rake Angle of Tool)*cos(Approach or Entering Angle)))
𝒊 = atan((tan(α_b)*sin(λ))-(tan(α_sr)*cos(λ)))
This formula uses 4 Functions, 4 Variables

Functions Used

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., sin(Angle)
cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., 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., 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., atan(Number)

Variables Used

Inclination Angle - (Measured in Radian) - Inclination Angle is the angle of inclination of the tool’s principal cutting edge from the reference plane and measured on the cutting plane.
Back Rake Angle - (Measured in Radian) - 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.
Approach or Entering Angle - (Measured in Radian) - 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.
Side Rake Angle of Tool - (Measured in Radian) - 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.

STEP 1: Convert Input(s) to Base Unit

Back Rake Angle: 36.3871 Degree --> 0.635074700252309 Radian (Check conversion here)
Approach or Entering Angle: 15 Degree --> 0.2617993877991 Radian (Check conversion here)
Side Rake Angle of Tool: 9.1631 Degree --> 0.159926264689462 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

𝒊 = atan((tan(α_b)*sin(λ))-(tan(α_sr)*cos(λ))) --> atan((tan(0.635074700252309)*sin(0.2617993877991))-(tan(0.159926264689462)*cos(0.2617993877991)))

Evaluating ... ...

𝒊 = 0.0349062289795786

STEP 3: Convert Result to Output's Unit

0.0349062289795786 Radian -->1.99997959924748 Degree (Check conversion here)

FINAL ANSWER

1.99997959924748 ≈ 1.99998 Degree <-- Inclination Angle

(Calculation completed in 00.004 seconds)

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Home » Engineering » Production Engineering » Metal Cutting » Metal Cutting Tools » Inclination Angle

Credits

Created by Vinay Mishra

Indian Institute for Aeronautical Engineering and Information Technology (IIAEIT), Pune

Vinay Mishra has created this Calculator and 300+ more calculators!

Verified by Rushi Shah

K J Somaiya College of Engineering (K J Somaiya), Mumbai

Rushi Shah has verified this Calculator and 200+ more calculators!

< 9 Metal Cutting Tools Calculators

Orthogonal Rake Angle

Go Orthogonal Rake Angle = arctan((tan(Side Rake Angle of Tool)*sin(Approach or Entering Angle))+(tan(Back Rake Angle)*cos(Approach or Entering Angle)))

Side Rake Angle

Go Side Rake Angle of Tool = atan((sin(Approach or Entering Angle)*tan(Orthogonal Rake Angle))-(cos(Approach or Entering Angle)*tan(Inclination Angle)))

Inclination Angle

Go Inclination Angle = atan((tan(Back Rake Angle)*sin(Approach or Entering Angle))-(tan(Side Rake Angle of Tool)*cos(Approach or Entering Angle)))

Back Rake Angle

Go Back Rake Angle = atan((cos(Approach or Entering Angle)*tan(Orthogonal Rake Angle))+(sin(Approach or Entering Angle)*tan(Inclination Angle)))

Required Tool Back Rake Angle given Angle Set from Axis B

Go Top Rake Angle = (atan(tan(Angle Set from Axis b)/cos(Side Rake Angle)))

Tool Side Rake Angle using Angle Set from Axis B

Go Side Rake Angle = (acos(tan(Angle Set from Axis b)/tan(Top Rake Angle)))

Angle set from axis B

Go Angle Set from Axis b = (atan(cos(Side Rake Angle)*tan(Top Rake Angle)))

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

Go Approach or Entering Angle = 1.5708-Side Cutting Edge Angle

Side cutting edge angle for given Lead (approach or entering) angle

Go Side Cutting Edge Angle = 1.5708-Approach or Entering Angle

Inclination Angle Formula

Inclination Angle = atan((tan(Back Rake Angle)*sin(Approach or Entering Angle))-(tan(Side Rake Angle of Tool)*cos(Approach or Entering Angle)))
𝒊 = atan((tan(α_b)*sin(λ))-(tan(α_sr)*cos(λ)))

What does zero inclination angle mean?

A zero inclination angle indicates that the Orthogonal Rake System and Normal Rake System are the same.

How to Calculate Inclination Angle?

Inclination Angle calculator 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 calculate 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 calculate Inclination Angle using this online calculator? To use this online calculator 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. Here is how the Inclination Angle calculation can be explained with given input values -> -1154.543898 = atan((tan(0.635074700252309)*sin(0.2617993877991))-(tan(0.159926264689462)*cos(0.2617993877991))).

FAQ

What is 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 and is represented as 𝒊 = atan((tan(α_b)*sin(λ))-(tan(α_sr)*cos(λ))) or Inclination Angle = atan((tan(Back Rake Angle)*sin(Approach or Entering Angle))-(tan(Side Rake Angle of Tool)*cos(Approach or Entering 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, 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 & 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.

How to calculate 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 is calculated using Inclination Angle = atan((tan(Back Rake Angle)*sin(Approach or Entering Angle))-(tan(Side Rake Angle of Tool)*cos(Approach or Entering Angle))). To calculate Inclination Angle, you need Back Rake Angle (α_b), Approach or Entering Angle (λ) & Side Rake Angle of Tool (α_sr). With our tool, you need to enter the respective value for Back Rake Angle, Approach or Entering Angle & Side Rake Angle of Tool and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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