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Uncut chip thickness given cutting force, shear stress, cut, friction, normal rake and shear angles Formula

GoUncut chip thickness for given width of cut, shear angle and area of shear plane Formula

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Uncut chip thickness in machining can be referred as the thickness of the undeformed chip. Check FAQs

t 1 = F cut \cdot \frac{\cos (ϕ + β - α)}{w c \cdot τ shear \cdot \cos (β - α)}

t₁ - Uncut Chip Thickness in Machining?F_cut - Cutting Force in Metal Cutting?ϕ - Shearing Angle?β - Cutting Friction Angle?α - Rake Angle of Cutting Tool?w_c - Cutting Width?τ_shear - Average Shear Stress Produced on Shear Plane?

Uncut chip thickness given cutting force, shear stress, cut, friction, normal rake and shear angles Example

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

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

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

6.94 = 314.677 \cdot \frac{\cos (5.257 + 67.48 - 8.58)}{9.6873 \cdot 3.95 \cdot \cos (67.48 - 8.58)}

6.94mm = 314.677N \cdot \frac{\cos (5.257° + 67.48° - 8.58°)}{9.6873mm \cdot 3.95MPa \cdot \cos (67.48° - 8.58°)}

6.94 = 314.677 \cdot \frac{\cos (5.257 + 67.48 - 8.58)}{9.6873 \cdot 3.95 \cdot \cos (67.48 - 8.58)}

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Uncut chip thickness given cutting force, shear stress, cut, friction, normal rake and shear angles Solution

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

FIRST Step Consider the formula

t 1 = F cut \cdot \frac{\cos (ϕ + β - α)}{w c \cdot τ shear \cdot \cos (β - α)}

Next Step Substitute values of Variables

∴

t 1 = 314.677N \cdot \frac{\cos (5.257° + 67.48° - 8.58°)}{9.6873mm \cdot 3.95MPa \cdot \cos (67.48° - 8.58°)}

Next Step Convert Units

∴

t 1 = 314.677N \cdot \frac{\cos (0.0918rad + 1.1777rad - 0.1497rad)}{0.0097m \cdot 4E+6Pa \cdot \cos (1.1777rad - 0.1497rad)}

Next Step Prepare to Evaluate

∴

t 1 = 314.677 \cdot \frac{\cos (0.0918 + 1.1777 - 0.1497)}{0.0097 \cdot 4E+6 \cdot \cos (1.1777 - 0.1497)}

Next Step Evaluate

∴

t 1 = 0.00694001341217083m

Next Step Convert to Output's Unit

∴

t 1 = 6.94001341217083mm

LAST Step Rounding Answer

∴

t 1 = 6.94mm

Uncut chip thickness given cutting force, shear stress, cut, friction, normal rake and shear angles Formula Elements

Variables

Functions

Uncut Chip Thickness in Machining

Uncut chip thickness in machining can be referred as the thickness of the undeformed chip.

Symbol: t₁

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Uncut Chip Thickness in Machining

Cutting Force in Metal Cutting

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

Symbol: F_cut

Measurement: ForceUnit: N

Note: Value should be greater than 0.

Formulas to find Cutting Force in Metal Cutting

Shearing Angle

Shearing angle between 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 Shearing Angle

Cutting Friction Angle

Cutting 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 Cutting Friction Angle

Rake Angle of Cutting Tool

Rake Angle of Cutting Tool 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 Rake Angle of Cutting Tool

Cutting Width

Cutting Width can be defined as the width the tool cuts into the workpiece.

Symbol: w_c

Measurement: LengthUnit: mm

Note: Value can be positive or negative.

Formulas to find Cutting Width

Average Shear Stress Produced on Shear Plane

Average shear stress produced on shear plane is the reaction of workpiece when applied to different cutting forces on an imaginary shear plane.

Symbol: τ_shear

Measurement: StressUnit: MPa

Note: Value can be positive or negative.

Formulas to find Average Shear Stress Produced on Shear Plane

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 to find Uncut Chip Thickness in Machining

Go Uncut chip thickness for given width of cut, shear angle and area of shear plane

t 1 = \frac{A s \cdot \sin (ϕ)}{w c}

Other formulas in Geometry and Dimensions category

Go Area of shear plane for given shear angle, width of cut and uncut chip thickness

A s = \frac{t 1 \cdot w c}{\sin (ϕ)}

Go Shear angle for given area of shear plane, width of cut and uncut chip thickness

ϕ = a \sin (w c \cdot \frac{t 1}{A s})

How to Evaluate Uncut chip thickness given cutting force, shear stress, cut, friction, normal rake and shear angles?

Uncut chip thickness given cutting force, shear stress, cut, friction, normal rake and shear angles evaluator uses Uncut Chip Thickness in Machining = Cutting Force in Metal Cutting*(cos(Shearing Angle+Cutting Friction Angle-Rake Angle of Cutting Tool))/(Cutting Width*Average Shear Stress Produced on Shear Plane*cos(Cutting Friction Angle-Rake Angle of Cutting Tool)) to evaluate the Uncut Chip Thickness in Machining, The Uncut chip thickness given cutting force, shear stress, cut, friction, normal 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 width of cut, Shear stress and cosine of difference of friction and rake angles. Uncut Chip Thickness in Machining is denoted by t₁ symbol.

How to evaluate Uncut chip thickness given cutting force, shear stress, cut, friction, normal rake and shear angles using this online evaluator? To use this online evaluator for Uncut chip thickness given cutting force, shear stress, cut, friction, normal rake and shear angles, enter Cutting Force in Metal Cutting (F_cut), Shearing Angle (ϕ), Cutting Friction Angle (β), Rake Angle of Cutting Tool (α), Cutting Width (w_c) & Average Shear Stress Produced on Shear Plane (τ_shear) and hit the calculate button.

FAQs on Uncut chip thickness given cutting force, shear stress, cut, friction, normal rake and shear angles

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

The formula of Uncut chip thickness given cutting force, shear stress, cut, friction, normal rake and shear angles is expressed as Uncut Chip Thickness in Machining = Cutting Force in Metal Cutting*(cos(Shearing Angle+Cutting Friction Angle-Rake Angle of Cutting Tool))/(Cutting Width*Average Shear Stress Produced on Shear Plane*cos(Cutting Friction Angle-Rake Angle of Cutting Tool)). Here is an example- 7248.517 = 314.677*(cos(0.0917519587773246+1.17774817924555-0.149749249821085))/(0.0096873*3950000*cos(1.17774817924555-0.149749249821085)).

How to calculate Uncut chip thickness given cutting force, shear stress, cut, friction, normal rake and shear angles?

With Cutting Force in Metal Cutting (F_cut), Shearing Angle (ϕ), Cutting Friction Angle (β), Rake Angle of Cutting Tool (α), Cutting Width (w_c) & Average Shear Stress Produced on Shear Plane (τ_shear) we can find Uncut chip thickness given cutting force, shear stress, cut, friction, normal rake and shear angles using the formula - Uncut Chip Thickness in Machining = Cutting Force in Metal Cutting*(cos(Shearing Angle+Cutting Friction Angle-Rake Angle of Cutting Tool))/(Cutting Width*Average Shear Stress Produced on Shear Plane*cos(Cutting Friction Angle-Rake Angle of Cutting Tool)). This formula also uses Cosine (cos) function(s).

What are the other ways to Calculate Uncut Chip Thickness in Machining?

Here are the different ways to Calculate Uncut Chip Thickness in Machining-

Uncut Chip Thickness in Machining=(Area of Shear Plane*sin(Shearing Angle))/Cutting Width

Can the Uncut chip thickness given cutting force, shear stress, cut, friction, normal rake and shear angles be negative?

No, the Uncut chip thickness given cutting force, shear stress, cut, friction, normal rake and shear angles, measured in Length cannot be negative.

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

Uncut chip thickness given cutting force, shear stress, cut, friction, normal rake and shear angles is usually measured using the Millimeter[mm] for Length. Meter[mm], Kilometer[mm], Decimeter[mm] are the few other units in which Uncut chip thickness given cutting force, shear stress, cut, friction, normal rake and shear angles can be measured.

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Uncut chip thickness given cutting force, shear stress, cut, friction, normal rake and shear angles Formula

​GoUncut chip thickness for given width of cut, shear angle and area of shear plane Formula

Uncut chip thickness given cutting force, shear stress, cut, friction, normal rake and shear angles Example

Uncut chip thickness given cutting force, shear stress, cut, friction, normal rake and shear angles Solution

Uncut chip thickness given cutting force, shear stress, cut, friction, normal rake and shear angles Formula Elements

Other Formulas to find Uncut Chip Thickness in Machining

Other formulas in Geometry and Dimensions category

How to Evaluate Uncut chip thickness given cutting force, shear stress, cut, friction, normal rake and shear angles?

FAQs on Uncut chip thickness given cutting force, shear stress, cut, friction, normal rake and shear angles

Variable Name

GoUncut chip thickness for given width of cut, shear angle and area of shear plane Formula