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Shear stress given cutting force, cut size, uncut chip thickness, friction, rake and shear angles Formula

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Average Shear Stress Induced on shear plane is the reaction of workpiece when applied to different cutting forces on an imaginary shear plane. Check FAQs

τ s = F' c \cdot \frac{\cos (ϕ' + β' - α')}{w cut \cdot t 1 \cdot \cos (β' - α')}

τ_s - Average Shear Stress Induced on Shear Plane?F'_c - Cutting Force on Workpiece?ϕ^' - Shear Angle for Metal Cutting?β^' - Machining Friction Angle?α^' - Cutting Tool Rake Angle?w_cut - Cutting Thickness?t₁ - Uncut Chip Width?

Shear stress given cutting force, cut size, uncut chip thickness, friction, rake and shear angles Example

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Here is how the Shear stress given cutting force, cut size, uncut chip thickness, friction, rake and shear angles equation looks like with Values.

Here is how the Shear stress given cutting force, cut size, uncut chip thickness, friction, rake and shear angles equation looks like with Units.

Here is how the Shear stress given cutting force, cut size, uncut chip thickness, friction, rake and shear angles equation looks like.

0.3788 = 150 \cdot \frac{\cos (27.3 + 36.695 - 8.6215)}{15 \cdot 17 \cdot \cos (36.695 - 8.6215)}

0.3788MPa = 150N \cdot \frac{\cos (27.3° + 36.695° - 8.6215°)}{15mm \cdot 17mm \cdot \cos (36.695° - 8.6215°)}

0.3788 = 150 \cdot \frac{\cos (27.3 + 36.695 - 8.6215)}{15 \cdot 17 \cdot \cos (36.695 - 8.6215)}

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Shear stress given cutting force, cut size, uncut chip thickness, friction, rake and shear angles Solution

Follow our step by step solution on how to calculate Shear stress given cutting force, cut size, uncut chip thickness, friction, rake and shear angles?

FIRST Step Consider the formula

τ s = F' c \cdot \frac{\cos (ϕ' + β' - α')}{w cut \cdot t 1 \cdot \cos (β' - α')}

Next Step Substitute values of Variables

∴

τ s = 150N \cdot \frac{\cos (27.3° + 36.695° - 8.6215°)}{15mm \cdot 17mm \cdot \cos (36.695° - 8.6215°)}

Next Step Convert Units

∴

τ s = 150N \cdot \frac{\cos (0.4765rad + 0.6404rad - 0.1505rad)}{0.015m \cdot 0.017m \cdot \cos (0.6404rad - 0.1505rad)}

Next Step Prepare to Evaluate

∴

τ s = 150 \cdot \frac{\cos (0.4765 + 0.6404 - 0.1505)}{0.015 \cdot 0.017 \cdot \cos (0.6404 - 0.1505)}

Next Step Evaluate

∴

τ s = 378819.835647425Pa

Next Step Convert to Output's Unit

∴

τ s = 0.378819835647424MPa

LAST Step Rounding Answer

∴

τ s = 0.3788MPa

Shear stress given cutting force, cut size, uncut chip thickness, friction, rake and shear angles Formula Elements

Variables

Functions

Average Shear Stress Induced on Shear Plane

Average Shear Stress Induced on shear plane is the reaction of workpiece when applied to different cutting forces on an imaginary shear plane.

Symbol: τ_s

Measurement: StressUnit: MPa

Note: Value can be positive or negative.

Formulas to find Average Shear Stress Induced on Shear Plane

Cutting Force on Workpiece

Cutting force on workpiece is the force in the direction of cutting, the same direction as the cutting speed.

Symbol: F'_c

Measurement: ForceUnit: N

Note: Value should be greater than 0.

Formulas to find Cutting Force on Workpiece

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

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

Cutting Thickness

Cutting thickness is referred 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 Cutting Thickness

Uncut Chip Width

Uncut chip width is the thickness of the undeformed chip.

Symbol: t₁

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Uncut Chip Width

cos

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

Syntax: cos(Angle)

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}

How to Evaluate Shear stress given cutting force, cut size, uncut chip thickness, friction, rake and shear angles?

Shear stress given cutting force, cut size, uncut chip thickness, friction, rake and shear angles evaluator uses Average Shear Stress Induced on Shear Plane = Cutting Force on Workpiece*(cos(Shear Angle for Metal Cutting+Machining Friction Angle-Cutting Tool Rake Angle))/(Cutting Thickness*Uncut Chip Width*cos(Machining Friction Angle-Cutting Tool Rake Angle)) to evaluate the Average Shear Stress Induced on Shear Plane, The Shear stress given cutting force, cut size, uncut chip thickness, friction, rake and shear angles formula is defined as cutting force multiplied by the cosine of summation of shear angle to the difference of friction and rake angles divided by the product of the uncut chip thickness, width of cut and cosine of difference of friction and rake angles. Average Shear Stress Induced on Shear Plane is denoted by τ_s symbol.

How to evaluate Shear stress given cutting force, cut size, uncut chip thickness, friction, rake and shear angles using this online evaluator? To use this online evaluator for Shear stress given cutting force, cut size, uncut chip thickness, friction, rake and shear angles, enter Cutting Force on Workpiece (F'_c), Shear Angle for Metal Cutting (ϕ^'), Machining Friction Angle (β^'), Cutting Tool Rake Angle (α^'), Cutting Thickness (w_cut) & Uncut Chip Width (t₁) and hit the calculate button.

FAQs on Shear stress given cutting force, cut size, uncut chip thickness, friction, rake and shear angles

What is the formula to find Shear stress given cutting force, cut size, uncut chip thickness, friction, rake and shear angles?

The formula of Shear stress given cutting force, cut size, uncut chip thickness, friction, rake and shear angles is expressed as Average Shear Stress Induced on Shear Plane = Cutting Force on Workpiece*(cos(Shear Angle for Metal Cutting+Machining Friction Angle-Cutting Tool Rake Angle))/(Cutting Thickness*Uncut Chip Width*cos(Machining Friction Angle-Cutting Tool Rake Angle)). Here is an example- 3.8E-7 = 150*(cos(0.476474885794362+0.640448569019199-0.150473561460663))/(0.015*0.017*cos(0.640448569019199-0.150473561460663)).

How to calculate Shear stress given cutting force, cut size, uncut chip thickness, friction, rake and shear angles?

With Cutting Force on Workpiece (F'_c), Shear Angle for Metal Cutting (ϕ^'), Machining Friction Angle (β^'), Cutting Tool Rake Angle (α^'), Cutting Thickness (w_cut) & Uncut Chip Width (t₁) we can find Shear stress given cutting force, cut size, uncut chip thickness, friction, rake and shear angles using the formula - Average Shear Stress Induced on Shear Plane = Cutting Force on Workpiece*(cos(Shear Angle for Metal Cutting+Machining Friction Angle-Cutting Tool Rake Angle))/(Cutting Thickness*Uncut Chip Width*cos(Machining Friction Angle-Cutting Tool Rake Angle)). This formula also uses Cosine (cos) function(s).

Can the Shear stress given cutting force, cut size, uncut chip thickness, friction, rake and shear angles be negative?

Yes, the Shear stress given cutting force, cut size, uncut chip thickness, friction, rake and shear angles, measured in Stress can be negative.

Which unit is used to measure Shear stress given cutting force, cut size, uncut chip thickness, friction, rake and shear angles?

Shear stress given cutting force, cut size, uncut chip thickness, friction, rake and shear angles is usually measured using the Megapascal[MPa] for Stress. Pascal[MPa], Newton per Square Meter[MPa], Newton per Square Millimeter[MPa] are the few other units in which Shear stress given cutting force, cut size, uncut chip thickness, friction, rake and shear angles can be measured.

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Shear stress given cutting force, cut size, uncut chip thickness, friction, rake and shear angles Formula

Shear stress given cutting force, cut size, uncut chip thickness, friction, rake and shear angles Example

Shear stress given cutting force, cut size, uncut chip thickness, friction, rake and shear angles Solution

Shear stress given cutting force, cut size, uncut chip thickness, friction, rake and shear angles Formula Elements

Other formulas in Resultants and Stress category

How to Evaluate Shear stress given cutting force, cut size, uncut chip thickness, friction, rake and shear angles?

FAQs on Shear stress given cutting force, cut size, uncut chip thickness, friction, rake and shear angles

Variable Name