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Normal stress due to tool Formula

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Normal Stress is stress that occurs when a member is loaded by an axial force. Check FAQs

σ n = \sin (ϕ) \cdot F r \cdot \frac{\sin ((ϕ + β - γ ne))}{A c}

σ_n - Normal Stress?ϕ - Shear Angle?F_r - Resultant Cutting Force?β - Mean Friction Angle on Tool Face?γ_ne - Working Normal Rake?A_c - Cross Sectional Area of Uncut Chip?

Normal stress due to tool Example

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Here is how the Normal stress due to tool equation looks like with Values.

Here is how the Normal stress due to tool equation looks like with Units.

Here is how the Normal stress due to tool equation looks like.

197.0968 = \sin (11.406) \cdot 647.55 \cdot \frac{\sin ((11.406 + 52.43 - 20))}{0.45}

197.0968N/mm² = \sin (11.406°) \cdot 647.55N \cdot \frac{\sin ((11.406° + 52.43° - 20°))}{0.45mm²}

197.0968 = \sin (11.406) \cdot 647.55 \cdot \frac{\sin ((11.406 + 52.43 - 20))}{0.45}

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Normal stress due to tool Solution

Follow our step by step solution on how to calculate Normal stress due to tool?

FIRST Step Consider the formula

σ n = \sin (ϕ) \cdot F r \cdot \frac{\sin ((ϕ + β - γ ne))}{A c}

Next Step Substitute values of Variables

∴

σ n = \sin (11.406°) \cdot 647.55N \cdot \frac{\sin ((11.406° + 52.43° - 20°))}{0.45mm²}

Next Step Convert Units

∴

σ n = \sin (0.1991rad) \cdot 647.55N \cdot \frac{\sin ((0.1991rad + 0.9151rad - 0.3491rad))}{4.5E-7m²}

Next Step Prepare to Evaluate

∴

σ n = \sin (0.1991) \cdot 647.55 \cdot \frac{\sin ((0.1991 + 0.9151 - 0.3491))}{4.5E-7}

Next Step Evaluate

∴

σ n = 197096787.182499Pa

Next Step Convert to Output's Unit

∴

σ n = 197.096787182499N/mm²

LAST Step Rounding Answer

∴

σ n = 197.0968N/mm²

Normal stress due to tool Formula Elements

Variables

Functions

Normal Stress

Normal Stress is stress that occurs when a member is loaded by an axial force.

Symbol: σ_n

Measurement: PressureUnit: N/mm²

Note: Value should be greater than 0.

Formulas to find Normal Stress

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

Resultant Cutting Force

The Resultant Cutting Force is the total force in the direction of cutting, the same direction as the cutting speed.

Symbol: F_r

Measurement: ForceUnit: N

Note: Value should be greater than 0.

Formulas to find Resultant Cutting Force

Mean Friction Angle on Tool Face

The Mean Friction Angle on Tool Face corresponds to the maximum static friction force between the tool face and workpiece.

Symbol: β

Measurement: AngleUnit: °

Note: Value should be greater than 0.

Formulas to find Mean Friction Angle on Tool Face

Working Normal Rake

The Working Normal Rake angle is the angle of orientation of the tool's rake surface from the reference plane and measured on a normal plane.

Symbol: γ_ne

Measurement: AngleUnit: °

Note: Value can be positive or negative.

Formulas to find Working Normal Rake

Cross Sectional Area of Uncut Chip

The Cross Sectional Area of Uncut Chip is the area enclosed within the outer surface of the workpiece and the line of cut followed by the single-point cutting edge. It is calculated for one pass.

Symbol: A_c

Measurement: AreaUnit: mm²

Note: Value should be greater than 0.

Formulas to find Cross Sectional Area of Uncut Chip

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 Forces and Friction category

Go Rate of Energy Consumption during Machining

P m = V cut \cdot F c

Go Cutting Speed using Rate of Energy Consumption during Machining

V cut = \frac{P m}{F c}

Go Specific cutting energy in machining

p s = \frac{P m}{Z w}

Go Rate of Energy Consumption during Machining given Specific Cutting Energy

P m = p s \cdot Z w

How to Evaluate Normal stress due to tool?

Normal stress due to tool evaluator uses Normal Stress = sin(Shear Angle)*Resultant Cutting Force*sin((Shear Angle+Mean Friction Angle on Tool Face-Working Normal Rake))/Cross Sectional Area of Uncut Chip to evaluate the Normal Stress, Normal stress due to tool is when a force acts perpendicular (or "normal") to the surface of a workpiece, it exerts normal stress. Normal Stress is denoted by σ_n symbol.

How to evaluate Normal stress due to tool using this online evaluator? To use this online evaluator for Normal stress due to tool, enter Shear Angle (ϕ), Resultant Cutting Force (F_r), Mean Friction Angle on Tool Face (β), Working Normal Rake (γ_ne) & Cross Sectional Area of Uncut Chip (A_c) and hit the calculate button.

FAQs on Normal stress due to tool

What is the formula to find Normal stress due to tool?

The formula of Normal stress due to tool is expressed as Normal Stress = sin(Shear Angle)*Resultant Cutting Force*sin((Shear Angle+Mean Friction Angle on Tool Face-Working Normal Rake))/Cross Sectional Area of Uncut Chip. Here is an example- 0.000197 = sin(0.199072254482436)*647.55*sin((0.199072254482436+0.915076126820455-0.3490658503988))/4.5E-07.

How to calculate Normal stress due to tool?

With Shear Angle (ϕ), Resultant Cutting Force (F_r), Mean Friction Angle on Tool Face (β), Working Normal Rake (γ_ne) & Cross Sectional Area of Uncut Chip (A_c) we can find Normal stress due to tool using the formula - Normal Stress = sin(Shear Angle)*Resultant Cutting Force*sin((Shear Angle+Mean Friction Angle on Tool Face-Working Normal Rake))/Cross Sectional Area of Uncut Chip. This formula also uses Sine (sin) function(s).

Can the Normal stress due to tool be negative?

No, the Normal stress due to tool, measured in Pressure cannot be negative.

Which unit is used to measure Normal stress due to tool?

Normal stress due to tool is usually measured using the Newton per Square Millimeter[N/mm²] for Pressure. Pascal[N/mm²], Kilopascal[N/mm²], Bar[N/mm²] are the few other units in which Normal stress due to tool can be measured.

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Normal stress due to tool Formula

Normal stress due to tool Example

Normal stress due to tool Solution

Normal stress due to tool Formula Elements

Other formulas in Forces and Friction category

How to Evaluate Normal stress due to tool?

FAQs on Normal stress due to tool

Variable Name