Pressure Acting on Rolls in Exit Region Calculator

✖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.ⓘ Mean Yield Shear Stress at Exit [S_y]			+10% -10%
✖Thickness at the given Point is defined as the thickness of stock at any point between entry and neutral point during the rolling.ⓘ Thickness at the given Point [h_x]			+10% -10%
✖Final Thickness is the thickness of the workpiece after rolling.ⓘ Final Thickness [h_ft]			+10% -10%
✖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.ⓘ Friction Coefficient [μ_r]			+10% -10%
✖Roll Radius is the distance between the center and the point on the circumference of the roller.ⓘ Roll Radius [R_roll]			+10% -10%
✖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.ⓘ Angle made by Point Roll Center and Normal [Θ_r]			+10% -10%

✖Pressure Acting on Exit is the force per unit area of Rollers on the sheet metal at the exit region.ⓘ Pressure Acting on Rolls in Exit Region [P_ex]

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Formula

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Pressure Acting on Rolls in Exit Region

Formula

`"P"_{"ex"} = "S"_{"y"}*"h"_{"x"}/"h"_{"ft"}*exp("μ"_{"r"}*2*sqrt("R"_{"roll"}/"h"_{"ft"})*atan("Θ"_{"r"}*sqrt("R"_{"roll"}/"h"_{"ft"})))`

Example

`"0.000459N/mm²"="22027.01"*"0.003135mm"/"7.3mm"*exp("0.6"*2*sqrt("100mm"/"7.3mm")*atan("18.5°"*sqrt("100mm"/"7.3mm")))`

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Pressure Acting on Rolls in Exit Region Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)))
P_ex = S_y*h_x/h_ft*exp(μ_r*2*sqrt(R_roll/h_ft)*atan(Θ_r*sqrt(R_roll/h_ft)))
This formula uses 4 Functions, 7 Variables

Functions Used

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., 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., 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., 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., sqrt(Number)

Variables Used

Pressure Acting on Exit - (Measured in Pascal) - Pressure Acting on Exit is the force per unit area of Rollers on the sheet metal at the exit region.
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.
Thickness at the given Point - (Measured in Meter) - Thickness at the given Point is defined as the thickness of stock at any point between entry and neutral point during the rolling.
Final Thickness - (Measured in Meter) - Final Thickness is the thickness of the workpiece after rolling.
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.
Roll Radius - (Measured in Meter) - Roll Radius is the distance between the center and the point on the circumference of the roller.
Angle made by Point Roll Center and Normal - (Measured in Radian) - 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.

STEP 1: Convert Input(s) to Base Unit

Mean Yield Shear Stress at Exit: 22027.01 --> No Conversion Required
Thickness at the given Point: 0.003135 Millimeter --> 3.135E-06 Meter (Check conversion here)
Final Thickness: 7.3 Millimeter --> 0.0073 Meter (Check conversion here)
Friction Coefficient: 0.6 --> No Conversion Required
Roll Radius: 100 Millimeter --> 0.1 Meter (Check conversion here)
Angle made by Point Roll Center and Normal: 18.5 Degree --> 0.32288591161889 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

P_ex = S_y*h_x/h_ft*exp(μ_r*2*sqrt(R_roll/h_ft)*atan(Θ_r*sqrt(R_roll/h_ft))) --> 22027.01*3.135E-06/0.0073*exp(0.6*2*sqrt(0.1/0.0073)*atan(0.32288591161889*sqrt(0.1/0.0073)))

Evaluating ... ...

P_ex = 458.941908980708

STEP 3: Convert Result to Output's Unit

458.941908980708 Pascal -->0.000458941908980708 Newton per Square Millimeter (Check conversion here)

FINAL ANSWER

0.000458941908980708 ≈ 0.000459 Newton per Square Millimeter <-- Pressure Acting on Exit

(Calculation completed in 00.004 seconds)

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< 4 Analysis at Exit Region Calculators

Pressure Acting on Rolls in Exit Region

Go 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)))

Mean Yield Shear Stress using Pressure on Exit Side

Go Mean Yield Shear Stress at Exit = (Pressure on Roller*Final Thickness)/(Thickness at the given Point*exp(Friction Coefficient*Factor H at given Point on Workpiece))

Thickness of Stock at given Point on Exit Side

Go Thickness at the given Point = (Pressure on Roller*Final Thickness)/(Mean Yield Shear Stress at Exit*exp(Friction Coefficient*Factor H at given Point on Workpiece))

Pressure on Rolls given H (Exit Side)

Go Pressure on Roller = Mean Yield Shear Stress at Exit*Thickness at the given Point/Final Thickness*exp(Friction Coefficient*Factor H at given Point on Workpiece)

Pressure Acting on Rolls in Exit Region Formula

How does pressure vary on rolls?

The pressure on rolls starts from the entry point and continues to build up till the neutral point. Similarly the exit pressure is zero at the exit point and increases towards the neutral point. At any section i, between the entry point and exit point in the rolls.

How to Calculate Pressure Acting on Rolls in Exit Region?

Pressure Acting on Rolls in Exit Region calculator 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 calculate 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 calculate Pressure Acting on Rolls in Exit Region using this online calculator? To use this online calculator 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. Here is how the Pressure Acting on Rolls in Exit Region calculation can be explained with given input values -> 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))).

FAQ

What is Pressure Acting on Rolls in Exit Region?

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 and is represented as P_ex = S_y*h_x/h_ft*exp(μ_r*2*sqrt(R_roll/h_ft)*atan(Θ_r*sqrt(R_roll/h_ft))) or 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))). 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, Thickness at the given Point is defined as the thickness of stock at any point between entry and neutral point during the rolling, Final Thickness is the thickness of the workpiece after rolling, 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, Roll Radius is the distance between the center and the point on the circumference of the roller & 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.

How to calculate Pressure Acting on Rolls in Exit Region?

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 is calculated using 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 calculate Pressure Acting on Rolls in Exit Region, you need 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). With our tool, you need to enter the respective value for Mean Yield Shear Stress at Exit, Thickness at the given Point, Final Thickness, Friction Coefficient, Roll Radius & Angle made by Point Roll Center and Normal and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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