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Shear angle for given Resultant force, force along shear force, friction, and normal rake angles Formula

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Shear angle in machining is the inclination of the shear plane with the horizontal axis at machining point. Check FAQs

ϕ = α rake - β friction + \arccos (\frac{F shr}{R o})

ϕ - Shear Angle in Machining?α_rake - Rake Angle in Machining?β_friction - Friction Angle in Machining?F_shr - Force Along Shear Plane in Machining?R_o - Resultant Force in Machining?

Shear angle for given Resultant force, force along shear force, friction, and normal rake angles Example

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

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

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

45 = 33 - 59 + \arccos (\frac{30.5}{93.6825})

45° = 33° - 59° + \arccos (\frac{30.5N}{93.6825N})

45 = 33 - 59 + \arccos (\frac{30.5}{93.6825})

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Shear angle for given Resultant force, force along shear force, friction, and normal rake angles Solution

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

FIRST Step Consider the formula

ϕ = α rake - β friction + \arccos (\frac{F shr}{R o})

Next Step Substitute values of Variables

∴

ϕ = 33° - 59° + \arccos (\frac{30.5N}{93.6825N})

Next Step Convert Units

∴

ϕ = 0.576rad - 1.0297rad + \arccos (\frac{30.5N}{93.6825N})

Next Step Prepare to Evaluate

∴

ϕ = 0.576 - 1.0297 + \arccos (\frac{30.5}{93.6825})

Next Step Evaluate

∴

ϕ = 0.785398599506867rad

Next Step Convert to Output's Unit

∴

ϕ = 45.0000249872375°

LAST Step Rounding Answer

∴

ϕ = 45°

Shear angle for given Resultant force, force along shear force, friction, and normal rake angles Formula Elements

Variables

Functions

Shear Angle in Machining

Shear angle in machining 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 in Machining

Rake Angle in Machining

Rake angle in machining the angle of orientation of tool’s rake surface from the reference plane and measured on machine longitudinal plane.

Symbol: α_rake

Measurement: AngleUnit: °

Note: Value can be positive or negative.

Formulas to find Rake Angle in Machining

Friction Angle in Machining

Friction angle in machining is termed as the angle between the tool and chip, which resists the flow of the chip along the rake face of the tool is friction force.

Symbol: β_friction

Measurement: AngleUnit: °

Note: Value should be greater than 0.

Formulas to find Friction Angle in Machining

Force Along Shear Plane in Machining

Force along shear plane in machining is the force acting along the shear plane.

Symbol: F_shr

Measurement: ForceUnit: N

Note: Value can be positive or negative.

Formulas to find Force Along Shear Plane in Machining

Resultant Force in Machining

Resultant force in machining is the vector sum of cutting force and thrust force.

Symbol: R_o

Measurement: ForceUnit: N

Note: Value should be greater than 0.

Formulas to find Resultant Force in Machining

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 Force Normal to Shear category

Go Force normal to shear force for given cutting force, thrust force, and shear angle

F N = F c \cdot \sin (ϕ) + P a \cdot \cos (ϕ)

Go Force normal to shear force for given mean normal shear stress and area of shear plane

F N = 𝜏 \cdot A

Go Cutting Shear Force given Uncut Chip Thickness and Shear Angle

F s = \frac{τ shr \cdot w cut \cdot t chip}{\sin (ϕ)}

How to Evaluate Shear angle for given Resultant force, force along shear force, friction, and normal rake angles?

Shear angle for given Resultant force, force along shear force, friction, and normal rake angles evaluator uses Shear Angle in Machining = Rake Angle in Machining-Friction Angle in Machining+arccos(Force Along Shear Plane in Machining/Resultant Force in Machining) to evaluate the Shear Angle in Machining, Shear angle for given Resultant force, force along shear force, friction, and normal rake angles is inclination between the shear plane and longitudinal plane. Shear Angle in Machining is denoted by ϕ symbol.

How to evaluate Shear angle for given Resultant force, force along shear force, friction, and normal rake angles using this online evaluator? To use this online evaluator for Shear angle for given Resultant force, force along shear force, friction, and normal rake angles, enter Rake Angle in Machining (α_rake), Friction Angle in Machining (β_friction), Force Along Shear Plane in Machining (F_shr) & Resultant Force in Machining (R_o) and hit the calculate button.

FAQs on Shear angle for given Resultant force, force along shear force, friction, and normal rake angles

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

The formula of Shear angle for given Resultant force, force along shear force, friction, and normal rake angles is expressed as Shear Angle in Machining = Rake Angle in Machining-Friction Angle in Machining+arccos(Force Along Shear Plane in Machining/Resultant Force in Machining). Here is an example- 2578.312 = 0.57595865315802-1.02974425867646+arccos(30.5/93.6825).

How to calculate Shear angle for given Resultant force, force along shear force, friction, and normal rake angles?

With Rake Angle in Machining (α_rake), Friction Angle in Machining (β_friction), Force Along Shear Plane in Machining (F_shr) & Resultant Force in Machining (R_o) we can find Shear angle for given Resultant force, force along shear force, friction, and normal rake angles using the formula - Shear Angle in Machining = Rake Angle in Machining-Friction Angle in Machining+arccos(Force Along Shear Plane in Machining/Resultant Force in Machining). This formula also uses Cosine (cos), Inverse Cosine (arccos) function(s).

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

No, the Shear angle for given Resultant force, force along shear force, friction, and normal rake angles, measured in Angle cannot be negative.

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

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

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Shear angle for given Resultant force, force along shear force, friction, and normal rake angles Formula

Shear angle for given Resultant force, force along shear force, friction, and normal rake angles Example

Shear angle for given Resultant force, force along shear force, friction, and normal rake angles Solution

Shear angle for given Resultant force, force along shear force, friction, and normal rake angles Formula Elements

Other formulas in Force Normal to Shear category

How to Evaluate Shear angle for given Resultant force, force along shear force, friction, and normal rake angles?

FAQs on Shear angle for given Resultant force, force along shear force, friction, and normal rake angles

Variable Name