Orthogonal Rake Angle Calculator

✖The Side Rake Angle 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 [α_s]			+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 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%

✖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]

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Formula

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Orthogonal Rake Angle

Formula

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

Example

`"37.00003°"=arctan((tan("9.1631°")*sin("15°"))+(tan("36.3871°")*cos("15°")))`

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Orthogonal Rake Angle Solution

STEP 0: Pre-Calculation Summary

Formula Used

Orthogonal Rake Angle = arctan((tan(Side Rake Angle)*sin(Approach or Entering Angle))+(tan(Back Rake Angle)*cos(Approach or Entering Angle)))
α = arctan((tan(α_s)*sin(λ))+(tan(α_b)*cos(λ)))
This formula uses 5 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)
ctan - Cotangent is a trigonometric function that is defined as the ratio of the adjacent side to the opposite side in a right triangle., 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)., arctan(Number)

Variables Used

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.
Side Rake Angle - (Measured in Radian) - The Side Rake Angle 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.
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.
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.

STEP 1: Convert Input(s) to Base Unit

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

STEP 2: Evaluate Formula

Substituting Input Values in Formula

α = arctan((tan(α_s)*sin(λ))+(tan(α_b)*cos(λ))) --> arctan((tan(0.159926264689462)*sin(0.2617993877991))+(tan(0.635074700252309)*cos(0.2617993877991)))

Evaluating ... ...

α = 0.64577230405488

STEP 3: Convert Result to Output's Unit

0.64577230405488 Radian -->37.0000275487905 Degree (Check conversion here)

FINAL ANSWER

37.0000275487905 ≈ 37.00003 Degree <-- Orthogonal Rake Angle

(Calculation completed in 00.004 seconds)

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Home » Engineering » Production Engineering » Metal Cutting » Metal Cutting Tools » Orthogonal 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

Orthogonal Rake Angle Formula

Orthogonal Rake Angle = arctan((tan(Side Rake Angle)*sin(Approach or Entering Angle))+(tan(Back Rake Angle)*cos(Approach or Entering Angle)))
α = arctan((tan(α_s)*sin(λ))+(tan(α_b)*cos(λ)))

What is Orthogonal Rake Angle?

A cutting plane is one that is perpendicular to the reference plane and contains the principal cutting edge of the turning tool. Another imaginary plane, which is perpendicular to both the reference plane and the cutting plane, is called the orthogonal plane. Therefore, the cutting plane, reference plane, and orthogonal plane are mutually perpendicular. The rake angle measured on this orthogonal plane is called the orthogonal rake angle.

How to Calculate Orthogonal Rake Angle?

Orthogonal Rake Angle calculator uses Orthogonal Rake Angle = arctan((tan(Side Rake Angle)*sin(Approach or Entering Angle))+(tan(Back Rake Angle)*cos(Approach or Entering Angle))) to calculate 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 calculate Orthogonal Rake Angle using this online calculator? To use this online calculator for Orthogonal Rake Angle, enter Side Rake Angle (α_s), Approach or Entering Angle (λ) & Back Rake Angle (α_b) and hit the calculate button. Here is how the Orthogonal Rake Angle calculation can be explained with given input values -> 2334.012 = arctan((tan(0.159926264689462)*sin(0.2617993877991))+(tan(0.635074700252309)*cos(0.2617993877991))).

FAQ

What is 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 and is represented as α = arctan((tan(α_s)*sin(λ))+(tan(α_b)*cos(λ))) or Orthogonal Rake Angle = arctan((tan(Side Rake Angle)*sin(Approach or Entering Angle))+(tan(Back Rake Angle)*cos(Approach or Entering Angle))). The Side Rake Angle 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, 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 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.

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