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Normal rake angle for given Resultant force, force along shear, shear, and friction angle Formula

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Cutting tool rake angle is the angle of orientation of tool’s rake surface from the reference plane and measured on machine longitudinal plane. Check FAQs

α' = ϕ' + β' - \arccos (\frac{F s}{R'})

α^' - Cutting Tool Rake Angle?ϕ^' - Shear Angle for Metal Cutting?β^' - Machining Friction Angle?F_s - Force Produced Along Shear Plane?R^' - Resultant Force on Workpiece?

Normal rake angle for given Resultant force, force along shear, shear, and friction angle Example

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Here is how the Normal rake angle for given Resultant force, force along shear, shear, and friction angle equation looks like with Values.

Here is how the Normal rake angle for given Resultant force, force along shear, shear, and friction angle equation looks like with Units.

Here is how the Normal rake angle for given Resultant force, force along shear, shear, and friction angle equation looks like.

8.6215 = 27.3 + 36.695 - \arccos (\frac{96.5982}{170})

8.6215° = 27.3° + 36.695° - \arccos (\frac{96.5982N}{170N})

8.6215 = 27.3 + 36.695 - \arccos (\frac{96.5982}{170})

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Normal rake angle for given Resultant force, force along shear, shear, and friction angle Solution

Follow our step by step solution on how to calculate Normal rake angle for given Resultant force, force along shear, shear, and friction angle?

FIRST Step Consider the formula

α' = ϕ' + β' - \arccos (\frac{F s}{R'})

Next Step Substitute values of Variables

∴

α' = 27.3° + 36.695° - \arccos (\frac{96.5982N}{170N})

Next Step Convert Units

∴

α' = 0.4765rad + 0.6404rad - \arccos (\frac{96.5982N}{170N})

Next Step Prepare to Evaluate

∴

α' = 0.4765 + 0.6404 - \arccos (\frac{96.5982}{170})

Next Step Evaluate

∴

α' = 0.150473939311218rad

Next Step Convert to Output's Unit

∴

α' = 8.6215216492421°

LAST Step Rounding Answer

∴

α' = 8.6215°

Normal rake angle for given Resultant force, force along shear, shear, and friction angle Formula Elements

Variables

Functions

Cutting Tool Rake Angle

Cutting tool rake angle is the angle of orientation of tool’s rake surface from the reference plane and measured on machine longitudinal plane.

Symbol: α^'

Measurement: AngleUnit: °

Note: Value can be positive or negative.

Formulas to find Cutting Tool Rake Angle

Shear Angle for Metal Cutting

Shear angle for metal cutting is the inclination of the shear plane with the horizontal axis at machining point.

Symbol: ϕ^'

Measurement: AngleUnit: °

Note: Value should be greater than 0.

Formulas to find Shear Angle for Metal Cutting

Machining Friction Angle

Machining friction angle is termed as the angle between the tool and chip, which resists the flow of the chip along the rake face of the tool.

Symbol: β^'

Measurement: AngleUnit: °

Note: Value should be greater than 0.

Formulas to find Machining Friction Angle

Force Produced Along Shear Plane

The force produced along shear plane is the internal force that causes material layers to slide past each other when subjected to shear stress.

Symbol: F_s

Measurement: ForceUnit: N

Note: Value can be positive or negative.

Formulas to find Force Produced Along Shear Plane

Resultant Force on Workpiece

Resultant force on workpiece is the vector sum of cutting force and thrust force.

Symbol: R^'

Measurement: ForceUnit: N

Note: Value can be positive or negative.

Formulas to find Resultant Force on Workpiece

cos

Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle.

Syntax: cos(Angle)

arccos

Arccosine function, is the inverse function of the cosine function.It is the function that takes a ratio as an input and returns the angle whose cosine is equal to that ratio.

Syntax: arccos(Number)

Other formulas in Resultants and Stress category

Go Force acting Normal to Rake Face given Cutting Force and Thrust Force

F N = F' c \cdot \cos (α' N) - F' t \cdot \sin (α' N)

Go Mean normal stress in shear plane for given normal force and shear area

σ n = \frac{F N}{A shear}

Go Resultant force in merchant circle for given cutting force, friction and normal rake angles

R' = F' c \cdot \sec (β' - α')

Go R in merchant circle for given force along shear force, shear, friction and normal rake angles

R' = F s \cdot \sec (ϕ' + β' - α')

How to Evaluate Normal rake angle for given Resultant force, force along shear, shear, and friction angle?

Normal rake angle for given Resultant force, force along shear, shear, and friction angle evaluator uses Cutting Tool Rake Angle = Shear Angle for Metal Cutting+Machining Friction Angle-arccos(Force Produced Along Shear Plane/Resultant Force on Workpiece) to evaluate the Cutting Tool Rake Angle, Normal rake angle for given Resultant force, force along shear, shear, and friction angles is defined as the angle of orientation of the tool's rake surface from the reference plane and measured on a normal plane. Cutting Tool Rake Angle is denoted by α^' symbol.

How to evaluate Normal rake angle for given Resultant force, force along shear, shear, and friction angle using this online evaluator? To use this online evaluator for Normal rake angle for given Resultant force, force along shear, shear, and friction angle, enter Shear Angle for Metal Cutting (ϕ^'), Machining Friction Angle (β^'), Force Produced Along Shear Plane (F_s) & Resultant Force on Workpiece (R^') and hit the calculate button.

FAQs on Normal rake angle for given Resultant force, force along shear, shear, and friction angle

What is the formula to find Normal rake angle for given Resultant force, force along shear, shear, and friction angle?

The formula of Normal rake angle for given Resultant force, force along shear, shear, and friction angle is expressed as Cutting Tool Rake Angle = Shear Angle for Metal Cutting+Machining Friction Angle-arccos(Force Produced Along Shear Plane/Resultant Force on Workpiece). Here is an example- 493.9768 = 0.476474885794362+0.640448569019199-arccos(96.5982/170).

How to calculate Normal rake angle for given Resultant force, force along shear, shear, and friction angle?

With Shear Angle for Metal Cutting (ϕ^'), Machining Friction Angle (β^'), Force Produced Along Shear Plane (F_s) & Resultant Force on Workpiece (R^') we can find Normal rake angle for given Resultant force, force along shear, shear, and friction angle using the formula - Cutting Tool Rake Angle = Shear Angle for Metal Cutting+Machining Friction Angle-arccos(Force Produced Along Shear Plane/Resultant Force on Workpiece). This formula also uses Cosine (cos), Inverse Cosine (arccos) function(s).

Can the Normal rake angle for given Resultant force, force along shear, shear, and friction angle be negative?

Yes, the Normal rake angle for given Resultant force, force along shear, shear, and friction angle, measured in Angle can be negative.

Which unit is used to measure Normal rake angle for given Resultant force, force along shear, shear, and friction angle?

Normal rake angle for given Resultant force, force along shear, shear, and friction angle is usually measured using the Degree[°] for Angle. Radian[°], Minute[°], Second[°] are the few other units in which Normal rake angle for given Resultant force, force along shear, shear, and friction angle can be measured.

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Normal rake angle for given Resultant force, force along shear, shear, and friction angle Formula

Normal rake angle for given Resultant force, force along shear, shear, and friction angle Example

Normal rake angle for given Resultant force, force along shear, shear, and friction angle Solution

Normal rake angle for given Resultant force, force along shear, shear, and friction angle Formula Elements

Other formulas in Resultants and Stress category

How to Evaluate Normal rake angle for given Resultant force, force along shear, shear, and friction angle?

FAQs on Normal rake angle for given Resultant force, force along shear, shear, and friction angle

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