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Cutting force for shear stress, width of cut, uncut chip thickness, friction, rake and shear angles Formula

GoCutting Force given Shear Force and Thrust Force Formula

GoCutting Force for Frictional Force along Tool Rake Face and Thrust Force Formula

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Force Exerted During Cutting is the force on workpiece in the direction of cutting, the same direction as the cutting speed. Check FAQs

F c = \frac{τ \cdot w \cdot t \cdot \cos (β - α)}{\cos (Φ + β - α)}

F_c - Force Exerted During Cutting?τ - Average Shear Stress on Shear Plane?w - Width of Cut?t - Uncut Chip Thickness?β - Friction Angle?α - Rake Angle?Φ - Shear Angle?

Cutting force for shear stress, width of cut, uncut chip thickness, friction, rake and shear angles Example

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Here is how the Cutting force for shear stress, width of cut, uncut chip thickness, friction, rake and shear angles equation looks like with Values.

Here is how the Cutting force for shear stress, width of cut, uncut chip thickness, friction, rake and shear angles equation looks like with Units.

Here is how the Cutting force for shear stress, width of cut, uncut chip thickness, friction, rake and shear angles equation looks like.

11.3392 = \frac{0.5 \cdot 14 \cdot 1.1656 \cdot \cos (25.79 - 1.95)}{\cos (25 + 25.79 - 1.95)}

11.3392N = \frac{0.5N/mm² \cdot 14mm \cdot 1.1656mm \cdot \cos (25.79° - 1.95°)}{\cos (25° + 25.79° - 1.95°)}

11.3392 = \frac{0.5 \cdot 14 \cdot 1.1656 \cdot \cos (25.79 - 1.95)}{\cos (25 + 25.79 - 1.95)}

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Cutting force for shear stress, width of cut, uncut chip thickness, friction, rake and shear angles Solution

Follow our step by step solution on how to calculate Cutting force for shear stress, width of cut, uncut chip thickness, friction, rake and shear angles?

FIRST Step Consider the formula

F c = \frac{τ \cdot w \cdot t \cdot \cos (β - α)}{\cos (Φ + β - α)}

Next Step Substitute values of Variables

∴

F c = \frac{0.5N/mm² \cdot 14mm \cdot 1.1656mm \cdot \cos (25.79° - 1.95°)}{\cos (25° + 25.79° - 1.95°)}

Next Step Convert Units

∴

F c = \frac{500000Pa \cdot 0.014m \cdot 0.0012m \cdot \cos (0.4501rad - 0.034rad)}{\cos (0.4363rad + 0.4501rad - 0.034rad)}

Next Step Prepare to Evaluate

∴

F c = \frac{500000 \cdot 0.014 \cdot 0.0012 \cdot \cos (0.4501 - 0.034)}{\cos (0.4363 + 0.4501 - 0.034)}

Next Step Evaluate

∴

F c = 11.3391772570935N

LAST Step Rounding Answer

∴

F c = 11.3392N

Cutting force for shear stress, width of cut, uncut chip thickness, friction, rake and shear angles Formula Elements

Variables

Functions

Force Exerted During Cutting

Force Exerted During Cutting is the force on workpiece 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 Force Exerted During Cutting

Average Shear Stress on Shear Plane

Average Shear Stress on Shear Plane is the average shear stress induced at imaginary shear plane.

Symbol: τ

Measurement: StressUnit: N/mm²

Note: Value can be positive or negative.

Formulas to find Average Shear Stress on Shear Plane

Width of Cut

The width of cut is defined as the width the tool cuts into the workpiece.

Symbol: w

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Width of Cut

Uncut Chip Thickness

Uncut Chip Thickness is the thickness of the undeformed chip.

Symbol: t

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Uncut Chip Thickness

Friction Angle

The Friction angle is termed as the force between the tool and chip, which resists the flow of the chip along the rake face of the tool is friction force and having a friction angle β.

Symbol: β

Measurement: AngleUnit: °

Note: Value can be positive or negative.

Formulas to find Friction Angle

Rake Angle

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 Rake Angle

Shear Angle

Shear angle 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

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 Force Exerted During Cutting

Go Cutting Force given Shear Force and Thrust Force

F c = \frac{F s + (F T \cdot \sin (Φ))}{\cos (Φ)}

Go Cutting Force for Frictional Force along Tool Rake Face and Thrust Force

F c = \frac{F - (F T \cdot (\cos (α o)))}{\sin (α o)}

How to Evaluate Cutting force for shear stress, width of cut, uncut chip thickness, friction, rake and shear angles?

Cutting force for shear stress, width of cut, uncut chip thickness, friction, rake and shear angles evaluator uses Force Exerted During Cutting = (Average Shear Stress on Shear Plane*Width of Cut*Uncut Chip Thickness*cos(Friction Angle-Rake Angle))/(cos(Shear Angle+Friction Angle-Rake Angle)) to evaluate the Force Exerted During Cutting, Cutting force for shear stress, width of cut, uncut chip thickness, friction, rake and shear angles is defined as the product of average shear stress along the shear planes, uncut chip thickness, and width of cut to the ratio of the cosine of difference of friction and rake angles to the cosine of shear angle added to difference of friction and rake angles. Force Exerted During Cutting is denoted by F_c symbol.

How to evaluate Cutting force for shear stress, width of cut, uncut chip thickness, friction, rake and shear angles using this online evaluator? To use this online evaluator for Cutting force for shear stress, width of cut, uncut chip thickness, friction, rake and shear angles, enter Average Shear Stress on Shear Plane (τ), Width of Cut (w), Uncut Chip Thickness (t), Friction Angle (β), Rake Angle (α) & Shear Angle (Φ) and hit the calculate button.

FAQs on Cutting force for shear stress, width of cut, uncut chip thickness, friction, rake and shear angles

What is the formula to find Cutting force for shear stress, width of cut, uncut chip thickness, friction, rake and shear angles?

The formula of Cutting force for shear stress, width of cut, uncut chip thickness, friction, rake and shear angles is expressed as Force Exerted During Cutting = (Average Shear Stress on Shear Plane*Width of Cut*Uncut Chip Thickness*cos(Friction Angle-Rake Angle))/(cos(Shear Angle+Friction Angle-Rake Angle)). Here is an example- 11.33918 = (500000*0.014*0.0011656*cos(0.450120414089253-0.034033920413883))/(cos(0.4363323129985+0.450120414089253-0.034033920413883)).

How to calculate Cutting force for shear stress, width of cut, uncut chip thickness, friction, rake and shear angles?

With Average Shear Stress on Shear Plane (τ), Width of Cut (w), Uncut Chip Thickness (t), Friction Angle (β), Rake Angle (α) & Shear Angle (Φ) we can find Cutting force for shear stress, width of cut, uncut chip thickness, friction, rake and shear angles using the formula - Force Exerted During Cutting = (Average Shear Stress on Shear Plane*Width of Cut*Uncut Chip Thickness*cos(Friction Angle-Rake Angle))/(cos(Shear Angle+Friction Angle-Rake Angle)). This formula also uses Cosine (cos) function(s).

What are the other ways to Calculate Force Exerted During Cutting?

Here are the different ways to Calculate Force Exerted During Cutting-

Force Exerted During Cutting=(Force Along Shear Force+(Thrust force in Machining*sin(Shear Angle)))/(cos(Shear Angle))
Force Exerted During Cutting=(Frictional Force in Machining-(Thrust force in Machining*(cos(Orthogonal Rake Angle))))/(sin(Orthogonal Rake Angle))
Force Exerted During Cutting=(Force Normal to Shear Force+Thrust force in Machining*sin(Orthogonal Rake Angle))/cos(Orthogonal Rake Angle)

Can the Cutting force for shear stress, width of cut, uncut chip thickness, friction, rake and shear angles be negative?

No, the Cutting force for shear stress, width of cut, uncut chip thickness, friction, rake and shear angles, measured in Force cannot be negative.

Which unit is used to measure Cutting force for shear stress, width of cut, uncut chip thickness, friction, rake and shear angles?

Cutting force for shear stress, width of cut, uncut chip thickness, friction, rake and shear angles is usually measured using the Newton[N] for Force. Exanewton[N], Meganewton[N], Kilonewton[N] are the few other units in which Cutting force for shear stress, width of cut, uncut chip thickness, friction, rake and shear angles can be measured.

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Cutting force for shear stress, width of cut, uncut chip thickness, friction, rake and shear angles Formula

​GoCutting Force given Shear Force and Thrust Force Formula

​GoCutting Force for Frictional Force along Tool Rake Face and Thrust Force Formula

Cutting force for shear stress, width of cut, uncut chip thickness, friction, rake and shear angles Example

Cutting force for shear stress, width of cut, uncut chip thickness, friction, rake and shear angles Solution

Cutting force for shear stress, width of cut, uncut chip thickness, friction, rake and shear angles Formula Elements

Other Formulas to find Force Exerted During Cutting

How to Evaluate Cutting force for shear stress, width of cut, uncut chip thickness, friction, rake and shear angles?

FAQs on Cutting force for shear stress, width of cut, uncut chip thickness, friction, rake and shear angles

Variable Name

GoCutting Force given Shear Force and Thrust Force Formula

GoCutting Force for Frictional Force along Tool Rake Face and Thrust Force Formula