Side 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 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]

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Formula

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Side Rake Angle

Formula

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

Example

`"9.16307°"=atan((sin("15°")*tan("37°"))-(cos("15°")*tan("2°")))`

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Side Rake Angle Solution

STEP 0: Pre-Calculation Summary

Formula Used

Side Rake Angle = atan((sin(Approach or Entering Angle)*tan(Orthogonal Rake Angle))-(cos(Approach or Entering Angle)*tan(Inclination Angle)))
α_s = atan((sin(λ)*tan(α))-(cos(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

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

Evaluating ... ...

α_s = 0.159925738912531

STEP 3: Convert Result to Output's Unit

0.159925738912531 Radian -->9.16306987520086 Degree (Check conversion here)

FINAL ANSWER

9.16306987520086 ≈ 9.16307 Degree <-- Side Rake Angle

(Calculation completed in 00.004 seconds)

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Home » Engineering » Production Engineering » Metal Cutting » Metal Cutting Tools » Side 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

Side Rake Angle Formula

Side Rake Angle = atan((sin(Approach or Entering Angle)*tan(Orthogonal Rake Angle))-(cos(Approach or Entering Angle)*tan(Inclination Angle)))
α_s = atan((sin(λ)*tan(α))-(cos(λ)*tan(𝒊)))

Can the side rake angle of a cutting tool be negative?

If the tool has a negative side-rake angle, it would generate much heat during cutting and have a shorter life. For this reason, the side-rake angle is usually as large as reasonably possible in the positive direction. Of course, if the side-rake angle is too large, the cutting edge will be weakened.
Sometimes, an extremely strong tool is required to withstand severe cutting loads. If both the side-rake angle and the back-rake angle is ground in the negative direction, the tool can cut very hard and tough materials, and it can take interrupted cuts. So, the side rake angle of a cutting tool can be negative.

How to Calculate Side Rake Angle?

Side Rake Angle calculator uses Side Rake Angle = atan((sin(Approach or Entering Angle)*tan(Orthogonal Rake Angle))-(cos(Approach or Entering Angle)*tan(Inclination Angle))) to calculate the Side Rake Angle, The Side Rake Angle is defined as the inclination of the face toward or away from the side cutting edge. Side Rake Angle is denoted by α_s symbol.

How to calculate Side Rake Angle using this online calculator? To use this online calculator for Side Rake Angle, enter Approach or Entering Angle (λ), Orthogonal Rake Angle (α) & Inclination Angle (𝒊) and hit the calculate button. Here is how the Side Rake Angle calculation can be explained with given input values -> 525.0052 = atan((sin(0.2617993877991)*tan(0.64577182323778))-(cos(0.2617993877991)*tan(0.03490658503988))).

FAQ

What is Side Rake Angle?

The Side Rake Angle is defined as the inclination of the face toward or away from the side cutting edge and is represented as α_s = atan((sin(λ)*tan(α))-(cos(λ)*tan(𝒊))) or Side Rake Angle = atan((sin(Approach or Entering Angle)*tan(Orthogonal Rake Angle))-(cos(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 Side Rake Angle?

The Side Rake Angle is defined as the inclination of the face toward or away from the side cutting edge is calculated using Side Rake Angle = atan((sin(Approach or Entering Angle)*tan(Orthogonal Rake Angle))-(cos(Approach or Entering Angle)*tan(Inclination Angle))). To calculate Side 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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