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Pressure Acting on Rolls in Exit Region Formula

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Pressure Acting on Exit is the force per unit area of Rollers on the sheet metal at the exit region. Check FAQs

P ex = S y \cdot \frac{h x}{h ft} \cdot \exp (μ r \cdot 2 \cdot \sqrt{\frac{R roll}{h ft}} \cdot a \tan (Θ r \cdot \sqrt{\frac{R roll}{h ft}}))

P_ex - Pressure Acting on Exit?S_y - Mean Yield Shear Stress at Exit?h_x - Thickness at the given Point?h_ft - Final Thickness?μ_r - Friction Coefficient?R_roll - Roll Radius?Θ_r - Angle made by Point Roll Center and Normal?

Pressure Acting on Rolls in Exit Region Example

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Here is how the Pressure Acting on Rolls in Exit Region equation looks like with Values.

Here is how the Pressure Acting on Rolls in Exit Region equation looks like with Units.

Here is how the Pressure Acting on Rolls in Exit Region equation looks like.

0.0005 = 22027.01 \cdot \frac{0.0031}{7.3} \cdot \exp (0.6 \cdot 2 \cdot \sqrt{\frac{100}{7.3}} \cdot a \tan (18.5 \cdot \sqrt{\frac{100}{7.3}}))

0.0005N/mm² = 22027.01Pa \cdot \frac{0.0031mm}{7.3mm} \cdot \exp (0.6 \cdot 2 \cdot \sqrt{\frac{100mm}{7.3mm}} \cdot a \tan (18.5° \cdot \sqrt{\frac{100mm}{7.3mm}}))

0.0005 = 22027.01 \cdot \frac{0.0031}{7.3} \cdot \exp (0.6 \cdot 2 \cdot \sqrt{\frac{100}{7.3}} \cdot a \tan (18.5 \cdot \sqrt{\frac{100}{7.3}}))

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Pressure Acting on Rolls in Exit Region Solution

Follow our step by step solution on how to calculate Pressure Acting on Rolls in Exit Region?

FIRST Step Consider the formula

P ex = S y \cdot \frac{h x}{h ft} \cdot \exp (μ r \cdot 2 \cdot \sqrt{\frac{R roll}{h ft}} \cdot a \tan (Θ r \cdot \sqrt{\frac{R roll}{h ft}}))

Next Step Substitute values of Variables

∴

P ex = 22027.01Pa \cdot \frac{0.0031mm}{7.3mm} \cdot \exp (0.6 \cdot 2 \cdot \sqrt{\frac{100mm}{7.3mm}} \cdot a \tan (18.5° \cdot \sqrt{\frac{100mm}{7.3mm}}))

Next Step Convert Units

∴

P ex = 22027.01Pa \cdot \frac{3.1E-6m}{0.0073m} \cdot \exp (0.6 \cdot 2 \cdot \sqrt{\frac{0.1m}{0.0073m}} \cdot a \tan (0.3229rad \cdot \sqrt{\frac{0.1m}{0.0073m}}))

Next Step Prepare to Evaluate

∴

P ex = 22027.01 \cdot \frac{3.1E-6}{0.0073} \cdot \exp (0.6 \cdot 2 \cdot \sqrt{\frac{0.1}{0.0073}} \cdot a \tan (0.3229 \cdot \sqrt{\frac{0.1}{0.0073}}))

Next Step Evaluate

∴

P ex = 458.941908980708Pa

Next Step Convert to Output's Unit

∴

P ex = 0.000458941908980708N/mm²

LAST Step Rounding Answer

∴

P ex = 0.0005N/mm²

Pressure Acting on Rolls in Exit Region Formula Elements

Variables

Functions

Pressure Acting on Exit

Pressure Acting on Exit is the force per unit area of Rollers on the sheet metal at the exit region.

Symbol: P_ex

Measurement: PressureUnit: N/mm²

Note: Value can be positive or negative.

Formulas to find Pressure Acting on Exit

Mean Yield Shear Stress at Exit

Mean Yield Shear Stress at Exit represents the average shear stress at which the material begins to yield or undergo plastic deformation at the end of rolling.

Symbol: S_y

Measurement: StressUnit: Pa

Note: Value should be greater than 0.

Formulas to find Mean Yield Shear Stress at Exit

Thickness at the given Point

Thickness at the given Point is defined as the thickness of stock at any point between entry and neutral point during the rolling.

Symbol: h_x

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Thickness at the given Point

Final Thickness

Final Thickness is the thickness of the workpiece after rolling.

Symbol: h_ft

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Final Thickness

Friction Coefficient

Friction Coefficient(μ) is the ratio defining the force that resists the motion of one body in relation to another body in contact with it.

Symbol: μ_r

Measurement: NAUnit: Unitless

Note: Value should be between 0 to 1.

Formulas to find Friction Coefficient

Roll Radius

Roll Radius is the distance between the center and the point on the circumference of the roller.

Symbol: R_roll

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Roll Radius

Angle made by Point Roll Center and Normal

Angle made by Point Roll Center and Normal refers to the angle between the roller centerline and the normal (vertical) to the surface of the material being rolled.

Symbol: Θ_r

Measurement: AngleUnit: °

Note: Value can be positive or negative.

Formulas to find Angle made by Point Roll Center and Normal

tan

The tangent of an angle is a trigonometric ratio of the length of the side opposite an angle to the length of the side adjacent to an angle in a right triangle.

Syntax: tan(Angle)

atan

Inverse tan is used to calculate the angle by applying the tangent ratio of the angle, which is the opposite side divided by the adjacent side of the right triangle.

Syntax: atan(Number)

exp

n an exponential function, the value of the function changes by a constant factor for every unit change in the independent variable.

Syntax: exp(Number)

sqrt

A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number.

Syntax: sqrt(Number)

Other formulas in Analysis at Exit Region category

Go Mean Yield Shear Stress using Pressure on Exit Side

S y = \frac{P rolls \cdot h ft}{h x \cdot \exp (μ r \cdot H)}

Go Pressure on Rolls given H (Exit Side)

P rolls = S y \cdot \frac{h x}{h ft} \cdot \exp (μ r \cdot H)

How to Evaluate Pressure Acting on Rolls in Exit Region?

Pressure Acting on Rolls in Exit Region evaluator uses Pressure Acting on Exit = Mean Yield Shear Stress at Exit*Thickness at the given Point/Final Thickness*exp(Friction Coefficient*2*sqrt(Roll Radius/Final Thickness)*atan(Angle made by Point Roll Center and Normal*sqrt(Roll Radius/Final Thickness))) to evaluate the Pressure Acting on Exit, Pressure Acting on Rolls in Exit Region is the pressure exerted on the sheet by the roll at the exit region, it is essential for reducing material thickness, controlling shape, improving surface finish, and minimizing defects. Pressure Acting on Exit is denoted by P_ex symbol.

How to evaluate Pressure Acting on Rolls in Exit Region using this online evaluator? To use this online evaluator for Pressure Acting on Rolls in Exit Region, enter Mean Yield Shear Stress at Exit (S_y), Thickness at the given Point (h_x), Final Thickness (h_ft), Friction Coefficient (μ_r), Roll Radius (R_roll) & Angle made by Point Roll Center and Normal (Θ_r) and hit the calculate button.

FAQs on Pressure Acting on Rolls in Exit Region

What is the formula to find Pressure Acting on Rolls in Exit Region?

The formula of Pressure Acting on Rolls in Exit Region is expressed as Pressure Acting on Exit = Mean Yield Shear Stress at Exit*Thickness at the given Point/Final Thickness*exp(Friction Coefficient*2*sqrt(Roll Radius/Final Thickness)*atan(Angle made by Point Roll Center and Normal*sqrt(Roll Radius/Final Thickness))). Here is an example- 4.6E-10 = 22027.01*3.135E-06/0.0073*exp(0.6*2*sqrt(0.1/0.0073)*atan(0.32288591161889*sqrt(0.1/0.0073))).

How to calculate Pressure Acting on Rolls in Exit Region?

With Mean Yield Shear Stress at Exit (S_y), Thickness at the given Point (h_x), Final Thickness (h_ft), Friction Coefficient (μ_r), Roll Radius (R_roll) & Angle made by Point Roll Center and Normal (Θ_r) we can find Pressure Acting on Rolls in Exit Region using the formula - Pressure Acting on Exit = Mean Yield Shear Stress at Exit*Thickness at the given Point/Final Thickness*exp(Friction Coefficient*2*sqrt(Roll Radius/Final Thickness)*atan(Angle made by Point Roll Center and Normal*sqrt(Roll Radius/Final Thickness))). This formula also uses Tangent (tan)Inverse Tan (atan)Exponential Growth (exp), Square Root (sqrt) function(s).

Can the Pressure Acting on Rolls in Exit Region be negative?

Yes, the Pressure Acting on Rolls in Exit Region, measured in Pressure can be negative.

Which unit is used to measure Pressure Acting on Rolls in Exit Region?

Pressure Acting on Rolls in Exit Region 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 Pressure Acting on Rolls in Exit Region can be measured.

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Pressure Acting on Rolls in Exit Region Formula

Pressure Acting on Rolls in Exit Region Example

Pressure Acting on Rolls in Exit Region Solution

Pressure Acting on Rolls in Exit Region Formula Elements

Other formulas in Analysis at Exit Region category

How to Evaluate Pressure Acting on Rolls in Exit Region?

FAQs on Pressure Acting on Rolls in Exit Region

Variable Name