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Required Tool Back Rake Angle given Angle Set from Axis B Formula

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The Top Rake Angle or Back 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. Check FAQs

α t = (a \tan (\frac{\tan (γ set)}{\cos (α s)}))

α_t - Top Rake Angle?γ_set - Angle Set from Axis b?α_s - Side Rake Angle?

Required Tool Back Rake Angle given Angle Set from Axis B Example

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Here is how the Required Tool Back Rake Angle given Angle Set from Axis B equation looks like with Values.

Here is how the Required Tool Back Rake Angle given Angle Set from Axis B equation looks like with Units.

Here is how the Required Tool Back Rake Angle given Angle Set from Axis B equation looks like.

10.9997 = (a \tan (\frac{\tan (10.83)}{\cos (10.2)}))

10.9997° = (a \tan (\frac{\tan (10.83°)}{\cos (10.2°)}))

10.9997 = (a \tan (\frac{\tan (10.83)}{\cos (10.2)}))

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Required Tool Back Rake Angle given Angle Set from Axis B Solution

Follow our step by step solution on how to calculate Required Tool Back Rake Angle given Angle Set from Axis B?

FIRST Step Consider the formula

α t = (a \tan (\frac{\tan (γ set)}{\cos (α s)}))

Next Step Substitute values of Variables

∴

α t = (a \tan (\frac{\tan (10.83°)}{\cos (10.2°)}))

Next Step Convert Units

∴

α t = (a \tan (\frac{\tan (0.189rad)}{\cos (0.178rad)}))

Next Step Prepare to Evaluate

∴

α t = (a \tan (\frac{\tan (0.189)}{\cos (0.178)}))

Next Step Evaluate

∴

α t = 0.191980991653683rad

Next Step Convert to Output's Unit

∴

α t = 10.9997005684944°

LAST Step Rounding Answer

∴

α t = 10.9997°

Required Tool Back Rake Angle given Angle Set from Axis B Formula Elements

Variables

Functions

Top Rake Angle

The Top Rake Angle or Back 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_t

Measurement: AngleUnit: °

Note: Value should be greater than 0.

Formulas to find Top Rake Angle

Angle Set from Axis b

Angle Set from Axis b is defined as the angle set by the tool from axis b.

Symbol: γ_set

Measurement: AngleUnit: °

Note: Value can be positive or negative.

Formulas to find Angle Set from Axis b

Side Rake 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.

Symbol: α_s

Measurement: AngleUnit: °

Note: Value should be greater than 0.

Formulas to find Side Rake 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 Inclination Angle

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

How to Evaluate Required Tool Back Rake Angle given Angle Set from Axis B?

Required Tool Back Rake Angle given Angle Set from Axis B evaluator uses Top Rake Angle = (atan(tan(Angle Set from Axis b)/cos(Side Rake Angle))) to evaluate the Top Rake Angle, The Required Tool Back Rake Angle given Angle Set from Axis B is the inclination of the face toward or away from the end of the end cutting edge of the tool. Top Rake Angle is denoted by α_t symbol.

How to evaluate Required Tool Back Rake Angle given Angle Set from Axis B using this online evaluator? To use this online evaluator for Required Tool Back Rake Angle given Angle Set from Axis B, enter Angle Set from Axis b (γ_set) & Side Rake Angle (α_s) and hit the calculate button.

FAQs on Required Tool Back Rake Angle given Angle Set from Axis B

What is the formula to find Required Tool Back Rake Angle given Angle Set from Axis B?

The formula of Required Tool Back Rake Angle given Angle Set from Axis B is expressed as Top Rake Angle = (atan(tan(Angle Set from Axis b)/cos(Side Rake Angle))). Here is an example- 629.8542 = (atan(tan(0.18901915799095)/cos(0.178023583703388))).

How to calculate Required Tool Back Rake Angle given Angle Set from Axis B?

With Angle Set from Axis b (γ_set) & Side Rake Angle (α_s) we can find Required Tool Back Rake Angle given Angle Set from Axis B using the formula - Top Rake Angle = (atan(tan(Angle Set from Axis b)/cos(Side Rake Angle))). This formula also uses Cosine (cos)Tangent (tan), Inverse Tan (atan) function(s).

Can the Required Tool Back Rake Angle given Angle Set from Axis B be negative?

No, the Required Tool Back Rake Angle given Angle Set from Axis B, measured in Angle cannot be negative.

Which unit is used to measure Required Tool Back Rake Angle given Angle Set from Axis B?

Required Tool Back Rake Angle given Angle Set from Axis B is usually measured using the Degree[°] for Angle. Radian[°], Minute[°], Second[°] are the few other units in which Required Tool Back Rake Angle given Angle Set from Axis B can be measured.

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Required Tool Back Rake Angle given Angle Set from Axis B Formula

Required Tool Back Rake Angle given Angle Set from Axis B Example

Required Tool Back Rake Angle given Angle Set from Axis B Solution

Required Tool Back Rake Angle given Angle Set from Axis B Formula Elements

Other formulas in Metal Cutting Tools category

How to Evaluate Required Tool Back Rake Angle given Angle Set from Axis B?

FAQs on Required Tool Back Rake Angle given Angle Set from Axis B

Variable Name