Back Rake Angle Calculator

✖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%
✖Orthogonal Rake Angle is the angle of orientation of the tool’s rake surface from the reference plane and measured on the orthogonal plane.ⓘ Orthogonal Rake Angle [α]			+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]			+10% -10%

✖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]

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Formula

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Back Rake Angle

Formula

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

Example

`"36.38708°"=atan((cos("15°")*tan("37°"))+(sin("15°")*tan("2°")))`

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Back Rake Angle Solution

STEP 0: Pre-Calculation Summary

Formula Used

Back Rake Angle = atan((cos(Approach or Entering Angle)*tan(Orthogonal Rake Angle))+(sin(Approach or Entering Angle)*tan(Inclination Angle)))
α_b = atan((cos(λ)*tan(α))+(sin(λ)*tan(𝒊)))
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

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.
Orthogonal Rake Angle - (Measured in Radian) - Orthogonal Rake Angle is the angle of orientation of the tool’s rake surface from the reference plane and measured on the orthogonal plane.
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.

STEP 1: Convert Input(s) to Base Unit

Approach or Entering Angle: 15 Degree --> 0.2617993877991 Radian (Check conversion here)
Orthogonal Rake Angle: 37 Degree --> 0.64577182323778 Radian (Check conversion here)
Inclination Angle: 2 Degree --> 0.03490658503988 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

α_b = atan((cos(λ)*tan(α))+(sin(λ)*tan(𝒊))) --> atan((cos(0.2617993877991)*tan(0.64577182323778))+(sin(0.2617993877991)*tan(0.03490658503988)))

Evaluating ... ...

α_b = 0.635074288150182

STEP 3: Convert Result to Output's Unit

0.635074288150182 Radian -->36.3870763882874 Degree (Check conversion here)

FINAL ANSWER

36.3870763882874 ≈ 36.38708 Degree <-- Back Rake Angle

(Calculation completed in 00.020 seconds)

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Home » Engineering » Production Engineering » Metal Cutting » Metal Cutting Tools » Back Rake 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 Anshika Arya

National Institute Of Technology (NIT), Hamirpur

Anshika Arya has verified this Calculator and 2500+ more calculators!

< 9 Metal Cutting Tools Calculators

Orthogonal Rake Angle

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

Side Rake Angle

Go Side Rake Angle = 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)*cos(Approach or Entering Angle)))

Required Tool Back Rake Angle given Angle Set from Axis B

Go Back 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(Back Rake Angle)))

Angle set from axis B

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

Back Rake Angle Formula

Back Rake Angle = atan((cos(Approach or Entering Angle)*tan(Orthogonal Rake Angle))+(sin(Approach or Entering Angle)*tan(Inclination Angle)))
α_b = atan((cos(λ)*tan(α))+(sin(λ)*tan(𝒊)))

What is the effect of the back rake angle?

The back rake angle affects the ability of the tool to shear the work material and form the chip which naturally curves into the work due to the difference in length from the outer and inner parts of the cut. It can be positive or negative.

How to Calculate Back Rake Angle?

Back Rake Angle calculator uses Back Rake Angle = atan((cos(Approach or Entering Angle)*tan(Orthogonal Rake Angle))+(sin(Approach or Entering Angle)*tan(Inclination Angle))) to calculate 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 calculate Back Rake Angle using this online calculator? To use this online calculator for Back Rake Angle, enter Approach or Entering Angle (λ), Orthogonal Rake Angle (α) & Inclination Angle (𝒊) and hit the calculate button. Here is how the Back Rake Angle calculation can be explained with given input values -> 3310.218 = atan((cos(0.2617993877991)*tan(0.64577182323778))+(sin(0.2617993877991)*tan(0.03490658503988))).

FAQ

What is 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 and is represented as α_b = atan((cos(λ)*tan(α))+(sin(λ)*tan(𝒊))) or Back Rake Angle = atan((cos(Approach or Entering Angle)*tan(Orthogonal Rake Angle))+(sin(Approach or Entering Angle)*tan(Inclination 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, Orthogonal Rake Angle is the angle of orientation of the tool’s rake surface from the reference plane and measured on the orthogonal plane & Inclination Angle is the angle of inclination of the tool’s principal cutting edge from the reference plane and measured on the cutting plane.

How to calculate 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 is calculated using Back Rake Angle = atan((cos(Approach or Entering Angle)*tan(Orthogonal Rake Angle))+(sin(Approach or Entering Angle)*tan(Inclination Angle))). To calculate Back Rake Angle, you need Approach or Entering Angle (λ), Orthogonal Rake Angle (α) & Inclination Angle (𝒊). With our tool, you need to enter the respective value for Approach or Entering Angle, Orthogonal Rake Angle & Inclination Angle 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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