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Pressure Acting on Rolls from Entry Side Formula

GoPressure on Rolls given H (Entry Side) Formula

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Pressure Acting at Entry is the force per unit area of Rollers on the sheet at the entry region. Check FAQs

P en = S e \cdot \frac{h e}{h in} \cdot \exp (μ rp \cdot (2 \cdot \sqrt{\frac{R roller}{h f}} \cdot a \tan (Θ r \cdot \sqrt{\frac{R roller}{h f}}) - 2 \cdot \sqrt{\frac{R roller}{h f}} \cdot a \tan (α bite \cdot \sqrt{\frac{R roller}{h f}})))

P_en - Pressure Acting at Entry?S_e - Mean Yield Shear Stress?h_e - Thickness at Entry?h_in - Initial Thickness?μ_rp - Coefficient of Friction?R_roller - Radius of Roller?h_f - Final Thickness after Rolling?Θ_r - Angle made by Point Roll Center and Normal?α_bite - Angle of Bite?

Pressure Acting on Rolls from Entry Side Example

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Here is how the Pressure Acting on Rolls from Entry Side equation looks like with Values.

Here is how the Pressure Acting on Rolls from Entry Side equation looks like with Units.

Here is how the Pressure Acting on Rolls from Entry Side equation looks like.

3.5E-6 = 4359.69 \cdot \frac{0.011}{3.5} \cdot \exp (0.5 \cdot (2 \cdot \sqrt{\frac{104}{7.5}} \cdot a \tan (18.5 \cdot \sqrt{\frac{104}{7.5}}) - 2 \cdot \sqrt{\frac{104}{7.5}} \cdot a \tan (45 \cdot \sqrt{\frac{104}{7.5}})))

3.5E-6N/mm² = 4359.69Pa \cdot \frac{0.011mm}{3.5mm} \cdot \exp (0.5 \cdot (2 \cdot \sqrt{\frac{104mm}{7.5mm}} \cdot a \tan (18.5° \cdot \sqrt{\frac{104mm}{7.5mm}}) - 2 \cdot \sqrt{\frac{104mm}{7.5mm}} \cdot a \tan (45° \cdot \sqrt{\frac{104mm}{7.5mm}})))

3.5E-6 = 4359.69 \cdot \frac{0.011}{3.5} \cdot \exp (0.5 \cdot (2 \cdot \sqrt{\frac{104}{7.5}} \cdot a \tan (18.5 \cdot \sqrt{\frac{104}{7.5}}) - 2 \cdot \sqrt{\frac{104}{7.5}} \cdot a \tan (45 \cdot \sqrt{\frac{104}{7.5}})))

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Pressure Acting on Rolls from Entry Side Solution

Follow our step by step solution on how to calculate Pressure Acting on Rolls from Entry Side?

FIRST Step Consider the formula

P en = S e \cdot \frac{h e}{h in} \cdot \exp (μ rp \cdot (2 \cdot \sqrt{\frac{R roller}{h f}} \cdot a \tan (Θ r \cdot \sqrt{\frac{R roller}{h f}}) - 2 \cdot \sqrt{\frac{R roller}{h f}} \cdot a \tan (α bite \cdot \sqrt{\frac{R roller}{h f}})))

Next Step Substitute values of Variables

∴

P en = 4359.69Pa \cdot \frac{0.011mm}{3.5mm} \cdot \exp (0.5 \cdot (2 \cdot \sqrt{\frac{104mm}{7.5mm}} \cdot a \tan (18.5° \cdot \sqrt{\frac{104mm}{7.5mm}}) - 2 \cdot \sqrt{\frac{104mm}{7.5mm}} \cdot a \tan (45° \cdot \sqrt{\frac{104mm}{7.5mm}})))

Next Step Convert Units

∴

P en = 4359.69Pa \cdot \frac{1.1E-5m}{0.0035m} \cdot \exp (0.5 \cdot (2 \cdot \sqrt{\frac{0.104m}{0.0075m}} \cdot a \tan (0.3229rad \cdot \sqrt{\frac{0.104m}{0.0075m}}) - 2 \cdot \sqrt{\frac{0.104m}{0.0075m}} \cdot a \tan (0.7854rad \cdot \sqrt{\frac{0.104m}{0.0075m}})))

Next Step Prepare to Evaluate

∴

P en = 4359.69 \cdot \frac{1.1E-5}{0.0035} \cdot \exp (0.5 \cdot (2 \cdot \sqrt{\frac{0.104}{0.0075}} \cdot a \tan (0.3229 \cdot \sqrt{\frac{0.104}{0.0075}}) - 2 \cdot \sqrt{\frac{0.104}{0.0075}} \cdot a \tan (0.7854 \cdot \sqrt{\frac{0.104}{0.0075}})))

Next Step Evaluate

∴

P en = 3.52861192729338Pa

Next Step Convert to Output's Unit

∴

P en = 3.52861192729338E-06N/mm²

LAST Step Rounding Answer

∴

P en = 3.5E-6N/mm²

Pressure Acting on Rolls from Entry Side Formula Elements

Variables

Functions

Pressure Acting at Entry

Pressure Acting at Entry is the force per unit area of Rollers on the sheet at the entry region.

Symbol: P_en

Measurement: PressureUnit: N/mm²

Note: Value can be positive or negative.

Formulas to find Pressure Acting at Entry

Mean Yield Shear Stress

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

Symbol: S_e

Measurement: StressUnit: Pa

Note: Value should be greater than 0.

Formulas to find Mean Yield Shear Stress

Thickness at Entry

Thickness at Entry is defined as the thickness of stock at any point between entry and neutral point.

Symbol: h_e

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Thickness at Entry

Initial Thickness

Initial Thickness is the thickness of sheet before the rolling operation.

Symbol: h_in

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Initial Thickness

Coefficient of Friction

Coefficient of Friction(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_rp

Measurement: NAUnit: Unitless

Note: Value should be between 0 to 1.

Formulas to find Coefficient of Friction

Radius of Roller

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

Symbol: R_roller

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Radius of Roller

Final Thickness after Rolling

Final Thickness after Rolling is the thickness of the workpiece after rolling process.

Symbol: h_f

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Final Thickness after Rolling

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

Angle of Bite

The angle of bite refers to the maximum attainable angle between the roll radius at the first contact and the roll centers during rolling of metals.

Symbol: α_bite

Measurement: AngleUnit: °

Note: Value can be positive or negative.

Formulas to find Angle of Bite

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 to find Pressure Acting at Entry

Go Pressure on Rolls given H (Entry Side)

P en = S e \cdot \frac{h e}{h in} \cdot \exp (μ rp \cdot (H in - H x))

Other formulas in Analysis at Entry Region category

Go Thickness of Stock at given Point on Entry Side

h e = \frac{P en \cdot h in}{S e \cdot \exp (μ rp \cdot (H in - H x))}

Go Mean Yield Shear Stress given Pressure on Entry Side

S e = \frac{P en \cdot \frac{h in}{h e}}{\exp (μ rp \cdot (H in - H x))}

How to Evaluate Pressure Acting on Rolls from Entry Side?

Pressure Acting on Rolls from Entry Side evaluator uses Pressure Acting at Entry = Mean Yield Shear Stress*Thickness at Entry/Initial Thickness*exp(Coefficient of Friction*(2*sqrt(Radius of Roller/Final Thickness after Rolling)*atan(Angle made by Point Roll Center and Normal*sqrt(Radius of Roller/Final Thickness after Rolling))-2*sqrt(Radius of Roller/Final Thickness after Rolling)*atan(Angle of Bite*sqrt(Radius of Roller/Final Thickness after Rolling)))) to evaluate the Pressure Acting at Entry, The Pressure acting on rolls from entry side is the pressure exerted on the sheet by the roll, it is essential for reducing material thickness, controlling shape, improving surface finish, and minimizing defects. Pressure Acting at Entry is denoted by P_en symbol.

How to evaluate Pressure Acting on Rolls from Entry Side using this online evaluator? To use this online evaluator for Pressure Acting on Rolls from Entry Side, enter Mean Yield Shear Stress (S_e), Thickness at Entry (h_e), Initial Thickness (h_in), Coefficient of Friction (μ_rp), Radius of Roller (R_roller), Final Thickness after Rolling (h_f), Angle made by Point Roll Center and Normal (Θ_r) & Angle of Bite (α_bite) and hit the calculate button.

FAQs on Pressure Acting on Rolls from Entry Side

What is the formula to find Pressure Acting on Rolls from Entry Side?

The formula of Pressure Acting on Rolls from Entry Side is expressed as Pressure Acting at Entry = Mean Yield Shear Stress*Thickness at Entry/Initial Thickness*exp(Coefficient of Friction*(2*sqrt(Radius of Roller/Final Thickness after Rolling)*atan(Angle made by Point Roll Center and Normal*sqrt(Radius of Roller/Final Thickness after Rolling))-2*sqrt(Radius of Roller/Final Thickness after Rolling)*atan(Angle of Bite*sqrt(Radius of Roller/Final Thickness after Rolling)))). Here is an example- 3.5E-12 = 4359.69*1.1E-05/0.0035*exp(0.5*(2*sqrt(0.104/0.0075)*atan(0.32288591161889*sqrt(0.104/0.0075))-2*sqrt(0.104/0.0075)*atan(0.785398163397301*sqrt(0.104/0.0075)))).

How to calculate Pressure Acting on Rolls from Entry Side?

With Mean Yield Shear Stress (S_e), Thickness at Entry (h_e), Initial Thickness (h_in), Coefficient of Friction (μ_rp), Radius of Roller (R_roller), Final Thickness after Rolling (h_f), Angle made by Point Roll Center and Normal (Θ_r) & Angle of Bite (α_bite) we can find Pressure Acting on Rolls from Entry Side using the formula - Pressure Acting at Entry = Mean Yield Shear Stress*Thickness at Entry/Initial Thickness*exp(Coefficient of Friction*(2*sqrt(Radius of Roller/Final Thickness after Rolling)*atan(Angle made by Point Roll Center and Normal*sqrt(Radius of Roller/Final Thickness after Rolling))-2*sqrt(Radius of Roller/Final Thickness after Rolling)*atan(Angle of Bite*sqrt(Radius of Roller/Final Thickness after Rolling)))). This formula also uses Tangent (tan)Inverse Tan (atan)Exponential Growth (exp), Square Root (sqrt) function(s).

What are the other ways to Calculate Pressure Acting at Entry?

Here are the different ways to Calculate Pressure Acting at Entry-

Pressure Acting at Entry=Mean Yield Shear Stress*Thickness at Entry/Initial Thickness*exp(Coefficient of Friction*(H Factor at Entry Point on Workpiece-Factor H at a Point on Workpiece))

Can the Pressure Acting on Rolls from Entry Side be negative?

Yes, the Pressure Acting on Rolls from Entry Side, measured in Pressure can be negative.

Which unit is used to measure Pressure Acting on Rolls from Entry Side?

Pressure Acting on Rolls from Entry Side 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 from Entry Side can be measured.

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Pressure Acting on Rolls from Entry Side Formula

​GoPressure on Rolls given H (Entry Side) Formula

Pressure Acting on Rolls from Entry Side Example

Pressure Acting on Rolls from Entry Side Solution

Pressure Acting on Rolls from Entry Side Formula Elements

Other Formulas to find Pressure Acting at Entry

Other formulas in Analysis at Entry Region category

How to Evaluate Pressure Acting on Rolls from Entry Side?

FAQs on Pressure Acting on Rolls from Entry Side

Variable Name

GoPressure on Rolls given H (Entry Side) Formula