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Cutting Shear Force given Uncut Chip Thickness and Shear Angle Formula

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Shear force in machining is the force which causes shear deformation to occur in the shear plane in metal cutting. Check FAQs

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

F_s - Shear Force in Machining?τ_shr - Shear Stress Induced on Job?w_cut - Thickness of Cut?t_chip - Uncut Chip Thickness?ϕ - Shear Angle in Machining?

Cutting Shear Force given Uncut Chip Thickness and Shear Angle Example

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Here is how the Cutting Shear Force given Uncut Chip Thickness and Shear Angle equation looks like with Values.

Here is how the Cutting Shear Force given Uncut Chip Thickness and Shear Angle equation looks like with Units.

Here is how the Cutting Shear Force given Uncut Chip Thickness and Shear Angle equation looks like.

95.0352 = \frac{14 \cdot 4 \cdot 1.2}{\sin (45)}

95.0352N = \frac{14MPa \cdot 4mm \cdot 1.2mm}{\sin (45°)}

95.0352 = \frac{14 \cdot 4 \cdot 1.2}{\sin (45)}

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Cutting Shear Force given Uncut Chip Thickness and Shear Angle Solution

Follow our step by step solution on how to calculate Cutting Shear Force given Uncut Chip Thickness and Shear Angle?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

F s = \frac{14MPa \cdot 4mm \cdot 1.2mm}{\sin (45°)}

Next Step Convert Units

∴

F s = \frac{1.4E+7Pa \cdot 0.004m \cdot 0.0012m}{\sin (0.7854rad)}

Next Step Prepare to Evaluate

∴

F s = \frac{1.4E+7 \cdot 0.004 \cdot 0.0012}{\sin (0.7854)}

Next Step Evaluate

∴

F s = 95.035151391486N

LAST Step Rounding Answer

∴

F s = 95.0352N

Cutting Shear Force given Uncut Chip Thickness and Shear Angle Formula Elements

Variables

Functions

Shear Force in Machining

Shear force in machining is the force which causes shear deformation to occur in the shear plane in metal cutting.

Symbol: F_s

Measurement: ForceUnit: N

Note: Value can be positive or negative.

Formulas to find Shear Force in Machining

Shear Stress Induced on Job

Shear stress induced on job force tending to cause deformation of a material by slippage along a plane or planes parallel to the imposed stress.

Symbol: τ_shr

Measurement: StressUnit: MPa

Note: Value should be greater than 0.

Formulas to find Shear Stress Induced on Job

Thickness of Cut

Thickness of cut can be defined as the thickness at which the tool cuts into the workpiece.

Symbol: w_cut

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Thickness of Cut

Uncut Chip Thickness

Uncut Chip Thickness is the thickness of the undeformed chip.

Symbol: t_chip

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Uncut Chip Thickness

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

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.

Syntax: sin(Angle)

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

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

How to Evaluate Cutting Shear Force given Uncut Chip Thickness and Shear Angle?

Cutting Shear Force given Uncut Chip Thickness and Shear Angle evaluator uses Shear Force in Machining = (Shear Stress Induced on Job*Thickness of Cut*Uncut Chip Thickness)/sin(Shear Angle in Machining) to evaluate the Shear Force in Machining, Cutting Shear Force given Uncut Chip Thickness and Shear Angle is the force which causes shear deformation to occur in the shear plane. Shear Force in Machining is denoted by F_s symbol.

How to evaluate Cutting Shear Force given Uncut Chip Thickness and Shear Angle using this online evaluator? To use this online evaluator for Cutting Shear Force given Uncut Chip Thickness and Shear Angle, enter Shear Stress Induced on Job (τ_shr), Thickness of Cut (w_cut), Uncut Chip Thickness (t_chip) & Shear Angle in Machining (ϕ) and hit the calculate button.

FAQs on Cutting Shear Force given Uncut Chip Thickness and Shear Angle

What is the formula to find Cutting Shear Force given Uncut Chip Thickness and Shear Angle?

The formula of Cutting Shear Force given Uncut Chip Thickness and Shear Angle is expressed as Shear Force in Machining = (Shear Stress Induced on Job*Thickness of Cut*Uncut Chip Thickness)/sin(Shear Angle in Machining). Here is an example- 95.03515 = (14000000*0.004*0.0012)/sin(0.785398163397301).

How to calculate Cutting Shear Force given Uncut Chip Thickness and Shear Angle?

With Shear Stress Induced on Job (τ_shr), Thickness of Cut (w_cut), Uncut Chip Thickness (t_chip) & Shear Angle in Machining (ϕ) we can find Cutting Shear Force given Uncut Chip Thickness and Shear Angle using the formula - Shear Force in Machining = (Shear Stress Induced on Job*Thickness of Cut*Uncut Chip Thickness)/sin(Shear Angle in Machining). This formula also uses Sine (sin) function(s).

Can the Cutting Shear Force given Uncut Chip Thickness and Shear Angle be negative?

Yes, the Cutting Shear Force given Uncut Chip Thickness and Shear Angle, measured in Force can be negative.

Which unit is used to measure Cutting Shear Force given Uncut Chip Thickness and Shear Angle?

Cutting Shear Force given Uncut Chip Thickness and Shear Angle is usually measured using the Newton[N] for Force. Exanewton[N], Meganewton[N], Kilonewton[N] are the few other units in which Cutting Shear Force given Uncut Chip Thickness and Shear Angle can be measured.

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Cutting Shear Force given Uncut Chip Thickness and Shear Angle Formula

Cutting Shear Force given Uncut Chip Thickness and Shear Angle Example

Cutting Shear Force given Uncut Chip Thickness and Shear Angle Solution

Cutting Shear Force given Uncut Chip Thickness and Shear Angle Formula Elements

Other formulas in Force Normal to Shear category

How to Evaluate Cutting Shear Force given Uncut Chip Thickness and Shear Angle?

FAQs on Cutting Shear Force given Uncut Chip Thickness and Shear Angle

Variable Name