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In a typical metal cutting operation, using a cutting tool of positive rake a = 10º. It was observed that the shear angle was 20º the friction angle is
- a)45º
- b)30º
- c)60º
- d)40º
Correct answer is option 'C'. Can you explain this answer?
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In a typical metal cutting operation, using a cutting tool of positive...
According to 1st earnest equation - Merchant theory
2(shear angle) + friction angle = 90degree + (rake angle) so friction angle is 60degree by solving by above values
2(shear angle) + friction angle = 90degree + (rake angle) so friction angle is 60degree by solving by above values
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In a typical metal cutting operation, using a cutting tool of positive...
The given problem is related to metal cutting operations and involves the determination of the friction angle based on the shear angle and rake angle values.
Shear Angle and Rake Angle:
- The shear angle (ϕ) in metal cutting refers to the angle between the direction of the cutting velocity and the resultant force acting on the shear plane.
- The rake angle (α) in metal cutting refers to the angle between the face of the cutting tool and a line perpendicular to the direction of cutting.
Given Data:
- Rake angle (α) = 10°
- Shear angle (ϕ) = 20°
Determination of Friction Angle:
To determine the friction angle (λ), we can use the relationship between the shear angle, rake angle, and friction angle, which is given by the equation:
tan(ϕ) = tan(α + λ)
In this equation, the shear angle is known (20°) and the rake angle is known (10°). By substituting these values into the equation, we can solve for the friction angle (λ).
tan(20°) = tan(10° + λ)
Taking the inverse tangent on both sides of the equation:
20° = 10° + λ
λ = 20° - 10°
λ = 10°
Therefore, the friction angle (λ) is 10°.
Correct Answer:
The correct answer is option 'C', which states that the friction angle is 60°. However, based on the calculations, the correct answer is actually 10°. Therefore, option 'C' is incorrect.
In summary, based on the given data, the shear angle is 20° and the rake angle is 10°. By using the relationship between shear angle, rake angle, and friction angle, we can determine the friction angle to be 10°, not 60° as stated in option 'C'.
Shear Angle and Rake Angle:
- The shear angle (ϕ) in metal cutting refers to the angle between the direction of the cutting velocity and the resultant force acting on the shear plane.
- The rake angle (α) in metal cutting refers to the angle between the face of the cutting tool and a line perpendicular to the direction of cutting.
Given Data:
- Rake angle (α) = 10°
- Shear angle (ϕ) = 20°
Determination of Friction Angle:
To determine the friction angle (λ), we can use the relationship between the shear angle, rake angle, and friction angle, which is given by the equation:
tan(ϕ) = tan(α + λ)
In this equation, the shear angle is known (20°) and the rake angle is known (10°). By substituting these values into the equation, we can solve for the friction angle (λ).
tan(20°) = tan(10° + λ)
Taking the inverse tangent on both sides of the equation:
20° = 10° + λ
λ = 20° - 10°
λ = 10°
Therefore, the friction angle (λ) is 10°.
Correct Answer:
The correct answer is option 'C', which states that the friction angle is 60°. However, based on the calculations, the correct answer is actually 10°. Therefore, option 'C' is incorrect.
In summary, based on the given data, the shear angle is 20° and the rake angle is 10°. By using the relationship between shear angle, rake angle, and friction angle, we can determine the friction angle to be 10°, not 60° as stated in option 'C'.
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In a typical metal cutting operation, using a cutting tool of positive rake a = 10. It was observed that the shear angle was 20 the friction angle isa)45b)30c)60d)40Correct answer is option 'C'. Can you explain this answer?
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