Pressure Acting on Rolls from Entry Side Calculator

✖Mean Yield Shear Stress represents the average shear stress at which the material begins to yield or undergo plastic deformation.ⓘ Mean Yield Shear Stress [S_e]			+10% -10%
✖Thickness at Entry is defined as the thickness of stock at any point between entry and neutral point.ⓘ Thickness at Entry [h_e]			+10% -10%
✖Initial Thickness is the thickness of sheet before the rolling operation.ⓘ Initial Thickness [h_in]			+10% -10%
✖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.ⓘ Coefficient of Friction [μ_rp]			+10% -10%
✖Radius of Roller is the distance between the center and the point on the circumference of the roller.ⓘ Radius of Roller [R_roller]			+10% -10%
✖Final Thickness after Rolling is the thickness of the workpiece after rolling process.ⓘ Final Thickness after Rolling [h_f]			+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%
✖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.ⓘ Angle of Bite [α_bite]			+10% -10%

✖Pressure Acting at Entry is the force per unit area of Rollers on the sheet at the entry region.ⓘ Pressure Acting on Rolls from Entry Side [P_e]

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Formula

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Pressure Acting on Rolls from Entry Side

Formula

`"P"_{"e"} = "S"_{"e"}*"h"_{"e"}/"h"_{"in"}*exp("μ"_{"rp"}*(2*sqrt("R"_{"roller"}/"h"_{"f"})*atan("Θ"_{"r"}*sqrt("R"_{"roller"}/"h"_{"f"}))-2*sqrt("R"_{"roller"}/"h"_{"f"})*atan("α"_{"bite"}*sqrt("R"_{"roller"}/"h"_{"f"}))))`

Example

`"3.5E^-6N/mm²"="4359.69"*"0.011mm"/"3.5mm"*exp("0.5"*(2*sqrt("104mm"/"7.5mm")*atan("18.5°"*sqrt("104mm"/"7.5mm"))-2*sqrt("104mm"/"7.5mm")*atan("45.00°"*sqrt("104mm"/"7.5mm"))))`

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Pressure Acting on Rolls from Entry Side Solution

STEP 0: Pre-Calculation Summary

Formula Used

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))))
P_e = S_e*h_e/h_in*exp(μ_rp*(2*sqrt(R_roller/h_f)*atan(Θ_r*sqrt(R_roller/h_f))-2*sqrt(R_roller/h_f)*atan(α_bite*sqrt(R_roller/h_f))))
This formula uses 4 Functions, 9 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 at Entry - (Measured in Pascal) - Pressure Acting at Entry is the force per unit area of Rollers on the sheet at the entry region.
Mean Yield Shear Stress - Mean Yield Shear Stress represents the average shear stress at which the material begins to yield or undergo plastic deformation.
Thickness at Entry - (Measured in Meter) - Thickness at Entry is defined as the thickness of stock at any point between entry and neutral point.
Initial Thickness - (Measured in Meter) - Initial Thickness is the thickness of sheet before the rolling operation.
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.
Radius of Roller - (Measured in Meter) - Radius of Roller is the distance between the center and the point on the circumference of the roller.
Final Thickness after Rolling - (Measured in Meter) - Final Thickness after Rolling is the thickness of the workpiece after rolling process.
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.
Angle of Bite - (Measured in Radian) - 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.

STEP 1: Convert Input(s) to Base Unit

Mean Yield Shear Stress: 4359.69 --> No Conversion Required
Thickness at Entry: 0.011 Millimeter --> 1.1E-05 Meter (Check conversion here)
Initial Thickness: 3.5 Millimeter --> 0.0035 Meter (Check conversion here)
Coefficient of Friction: 0.5 --> No Conversion Required
Radius of Roller: 104 Millimeter --> 0.104 Meter (Check conversion here)
Final Thickness after Rolling: 7.5 Millimeter --> 0.0075 Meter (Check conversion here)
Angle made by Point Roll Center and Normal: 18.5 Degree --> 0.32288591161889 Radian (Check conversion here)
Angle of Bite: 45 Degree --> 0.785398163397301 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

P_e = S_e*h_e/h_in*exp(μ_rp*(2*sqrt(R_roller/h_f)*atan(Θ_r*sqrt(R_roller/h_f))-2*sqrt(R_roller/h_f)*atan(α_bite*sqrt(R_roller/h_f)))) --> 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))))

Evaluating ... ...

P_e = 3.52861192729338

STEP 3: Convert Result to Output's Unit

3.52861192729338 Pascal -->3.52861192729338E-06 Newton per Square Millimeter (Check conversion here)

FINAL ANSWER

3.52861192729338E-06 ≈ 3.5E-6 Newton per Square Millimeter <-- Pressure Acting at Entry

(Calculation completed in 00.020 seconds)

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Home » Engineering » Production Engineering » Rolling Process » Analysis at Entry Region » Pressure Acting on Rolls from Entry Side

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< 4 Analysis at Entry Region Calculators

Pressure Acting on Rolls from Entry Side

Go 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))))

Mean Yield Shear Stress given Pressure on Entry Side

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

Thickness of Stock at given Point on Entry Side

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

Pressure on Rolls given H (Entry Side)

Go 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))

Pressure Acting on Rolls from Entry Side Formula

How does pressure on rolls vary?

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 from Entry Side?

Pressure Acting on Rolls from Entry Side calculator 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 calculate 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_e symbol.

How to calculate Pressure Acting on Rolls from Entry Side using this online calculator? To use this online calculator 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. Here is how the Pressure Acting on Rolls from Entry Side calculation can be explained with given input values -> 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)))).

FAQ

What is Pressure Acting on Rolls from Entry Side?

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 and is represented as P_e = S_e*h_e/h_in*exp(μ_rp*(2*sqrt(R_roller/h_f)*atan(Θ_r*sqrt(R_roller/h_f))-2*sqrt(R_roller/h_f)*atan(α_bite*sqrt(R_roller/h_f)))) or 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)))). Mean Yield Shear Stress represents the average shear stress at which the material begins to yield or undergo plastic deformation, Thickness at Entry is defined as the thickness of stock at any point between entry and neutral point, Initial Thickness is the thickness of sheet before the rolling operation, 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, Radius of Roller is the distance between the center and the point on the circumference of the roller, Final Thickness after Rolling is the thickness of the workpiece after rolling process, 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 & 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.

How to calculate Pressure Acting on Rolls from Entry Side?

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

How many ways are there to calculate Pressure Acting at Entry?

In this formula, Pressure Acting at Entry uses Mean Yield Shear Stress, Thickness at Entry, Initial Thickness, Coefficient of Friction, Radius of Roller, Final Thickness after Rolling, Angle made by Point Roll Center and Normal & Angle of Bite. We can use 1 other way(s) to calculate the same, which is/are as follows -

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))

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