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Pressure Considering Rolling Similar to Plane-Strain-Upsetting Process Formula

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Pressure Acting while Rolling is the force per unit area of Rollers/plates during the rolling process. Check FAQs

P r = b \cdot \frac{2 \cdot σ}{\sqrt{3}} \cdot (1 + \frac{μ sf \cdot R \cdot \frac{π}{180} \cdot α b}{2 \cdot (h i + h fi)}) \cdot R \cdot \frac{π}{180} \cdot α b

P_r - Pressure Acting while Rolling?b - Strip Width of Spiral Spring?σ - Flow Stress of Work Material?μ_sf - Frictional Shear Factor?R - Roller Radius?α_b - Bite Angle?h_i - Thickness before Rolling?h_fi - Thickness after Rolling?π - Archimedes' constant?

Pressure Considering Rolling Similar to Plane-Strain-Upsetting Process Example

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Here is how the Pressure Considering Rolling Similar to Plane-Strain-Upsetting Process equation looks like with Values.

Here is how the Pressure Considering Rolling Similar to Plane-Strain-Upsetting Process equation looks like with Units.

Here is how the Pressure Considering Rolling Similar to Plane-Strain-Upsetting Process equation looks like.

3.3E-5 = 14.5 \cdot \frac{2 \cdot 2.1}{\sqrt{3}} \cdot (1 + \frac{0.41 \cdot 102 \cdot \frac{3.1416}{180} \cdot 30}{2 \cdot (3.4 + 7.2)}) \cdot 102 \cdot \frac{3.1416}{180} \cdot 30

3.3E-5N/mm² = 14.5mm \cdot \frac{2 \cdot 2.1N/mm²}{\sqrt{3}} \cdot (1 + \frac{0.41 \cdot 102mm \cdot \frac{3.1416}{180} \cdot 30°}{2 \cdot (3.4mm + 7.2mm)}) \cdot 102mm \cdot \frac{3.1416}{180} \cdot 30°

3.3E-5 = 14.5 \cdot \frac{2 \cdot 2.1}{\sqrt{3}} \cdot (1 + \frac{0.41 \cdot 102 \cdot \frac{3.1416}{180} \cdot 30}{2 \cdot (3.4 + 7.2)}) \cdot 102 \cdot \frac{3.1416}{180} \cdot 30

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Pressure Considering Rolling Similar to Plane-Strain-Upsetting Process Solution

Follow our step by step solution on how to calculate Pressure Considering Rolling Similar to Plane-Strain-Upsetting Process?

FIRST Step Consider the formula

P r = b \cdot \frac{2 \cdot σ}{\sqrt{3}} \cdot (1 + \frac{μ sf \cdot R \cdot \frac{π}{180} \cdot α b}{2 \cdot (h i + h fi)}) \cdot R \cdot \frac{π}{180} \cdot α b

Next Step Substitute values of Variables

∴

P r = 14.5mm \cdot \frac{2 \cdot 2.1N/mm²}{\sqrt{3}} \cdot (1 + \frac{0.41 \cdot 102mm \cdot \frac{π}{180} \cdot 30°}{2 \cdot (3.4mm + 7.2mm)}) \cdot 102mm \cdot \frac{π}{180} \cdot 30°

Next Step Substitute values of Constants

∴

P r = 14.5mm \cdot \frac{2 \cdot 2.1N/mm²}{\sqrt{3}} \cdot (1 + \frac{0.41 \cdot 102mm \cdot \frac{3.1416}{180} \cdot 30°}{2 \cdot (3.4mm + 7.2mm)}) \cdot 102mm \cdot \frac{3.1416}{180} \cdot 30°

Next Step Convert Units

∴

P r = 0.0145m \cdot \frac{2 \cdot 2.1E+6Pa}{\sqrt{3}} \cdot (1 + \frac{0.41 \cdot 0.102m \cdot \frac{3.1416}{180} \cdot 0.5236rad}{2 \cdot (0.0034m + 0.0072m)}) \cdot 0.102m \cdot \frac{3.1416}{180} \cdot 0.5236rad

Next Step Prepare to Evaluate

∴

P r = 0.0145 \cdot \frac{2 \cdot 2.1E+6}{\sqrt{3}} \cdot (1 + \frac{0.41 \cdot 0.102 \cdot \frac{3.1416}{180} \cdot 0.5236}{2 \cdot (0.0034 + 0.0072)}) \cdot 0.102 \cdot \frac{3.1416}{180} \cdot 0.5236

Next Step Evaluate

∴

P r = 33.3650773318261Pa

Next Step Convert to Output's Unit

∴

P r = 3.33650773318261E-05N/mm²

LAST Step Rounding Answer

∴

P r = 3.3E-5N/mm²

Pressure Considering Rolling Similar to Plane-Strain-Upsetting Process Formula Elements

Variables

Constants

Functions

Pressure Acting while Rolling

Pressure Acting while Rolling is the force per unit area of Rollers/plates during the rolling process.

Symbol: P_r

Measurement: PressureUnit: N/mm²

Note: Value can be positive or negative.

Strip Width of Spiral Spring

Strip Width of Spiral Spring is defined as the thickness of the wired strip measured in the lateral direction and by which the spiral spring is manufactured.

Symbol: b

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Flow Stress of Work Material

Flow Stress of Work Material refers to the instantaneous value of stress required to continue deforming a material, effectively keeping the metal flowing.

Symbol: σ

Measurement: PressureUnit: N/mm²

Note: Value can be positive or negative.

Frictional Shear Factor

Frictional Shear Factor is generated by the interaction between the workpiece and rolls. It contributes to the overall deformation of the material.

Symbol: μ_sf

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Roller Radius

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

Symbol: R

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Bite Angle

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

Symbol: α_b

Measurement: AngleUnit: °

Note: Value can be positive or negative.

Thickness before Rolling

Thickness before Rolling is the thickness of sheet before rolling operation begins.

Symbol: h_i

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Thickness after Rolling

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

Symbol: h_fi

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

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)

Credits

Created by Rajat Vishwakarma

University Institute of Technology RGPV (UIT - RGPV), Bhopal

Rajat Vishwakarma has created this Formula and 400+ more formulas!

Verified by Anshika Arya

National Institute Of Technology (NIT), Hamirpur

Anshika Arya has verified this Formula and 2500+ more formulas!

Other formulas in Rolling Analysis category

Go Bite Angle

α b = a \cos (1 - \frac{h}{2 \cdot R})

Go Maximum Reduction in Thickness Possible

Δt = {μ f}^{2} \cdot R

How to Evaluate Pressure Considering Rolling Similar to Plane-Strain-Upsetting Process?

Pressure Considering Rolling Similar to Plane-Strain-Upsetting Process evaluator uses Pressure Acting while Rolling = Strip Width of Spiral Spring*(2*Flow Stress of Work Material)/sqrt(3)*(1+(Frictional Shear Factor*Roller Radius*pi/180*Bite Angle)/(2*(Thickness before Rolling+Thickness after Rolling)))*Roller Radius*pi/180*Bite Angle to evaluate the Pressure Acting while Rolling, The Pressure considering rolling similar to plane-strain-upsetting process formula is the pressure on rollers obtained on compressing a billet or workpiece between two dies. Pressure Acting while Rolling is denoted by P_r symbol.

How to evaluate Pressure Considering Rolling Similar to Plane-Strain-Upsetting Process using this online evaluator? To use this online evaluator for Pressure Considering Rolling Similar to Plane-Strain-Upsetting Process, enter Strip Width of Spiral Spring (b), Flow Stress of Work Material (σ), Frictional Shear Factor (μ_sf), Roller Radius (R), Bite Angle (α_b), Thickness before Rolling (h_i) & Thickness after Rolling (h_fi) and hit the calculate button.

FAQs on Pressure Considering Rolling Similar to Plane-Strain-Upsetting Process

What is the formula to find Pressure Considering Rolling Similar to Plane-Strain-Upsetting Process?

The formula of Pressure Considering Rolling Similar to Plane-Strain-Upsetting Process is expressed as Pressure Acting while Rolling = Strip Width of Spiral Spring*(2*Flow Stress of Work Material)/sqrt(3)*(1+(Frictional Shear Factor*Roller Radius*pi/180*Bite Angle)/(2*(Thickness before Rolling+Thickness after Rolling)))*Roller Radius*pi/180*Bite Angle. Here is an example- 3.3E-11 = 0.0145*(2*2100000)/sqrt(3)*(1+(0.41*0.102*pi/180*0.5235987755982)/(2*(0.0034+0.0072)))*0.102*pi/180*0.5235987755982.

How to calculate Pressure Considering Rolling Similar to Plane-Strain-Upsetting Process?

With Strip Width of Spiral Spring (b), Flow Stress of Work Material (σ), Frictional Shear Factor (μ_sf), Roller Radius (R), Bite Angle (α_b), Thickness before Rolling (h_i) & Thickness after Rolling (h_fi) we can find Pressure Considering Rolling Similar to Plane-Strain-Upsetting Process using the formula - Pressure Acting while Rolling = Strip Width of Spiral Spring*(2*Flow Stress of Work Material)/sqrt(3)*(1+(Frictional Shear Factor*Roller Radius*pi/180*Bite Angle)/(2*(Thickness before Rolling+Thickness after Rolling)))*Roller Radius*pi/180*Bite Angle. This formula also uses Archimedes' constant and Square Root (sqrt) function(s).

Can the Pressure Considering Rolling Similar to Plane-Strain-Upsetting Process be negative?

Yes, the Pressure Considering Rolling Similar to Plane-Strain-Upsetting Process, measured in Pressure can be negative.

Which unit is used to measure Pressure Considering Rolling Similar to Plane-Strain-Upsetting Process?

Pressure Considering Rolling Similar to Plane-Strain-Upsetting Process 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 Considering Rolling Similar to Plane-Strain-Upsetting Process can be measured.

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Pressure Considering Rolling Similar to Plane-Strain-Upsetting Process Formula

Pressure Considering Rolling Similar to Plane-Strain-Upsetting Process Example

Pressure Considering Rolling Similar to Plane-Strain-Upsetting Process Solution

Pressure Considering Rolling Similar to Plane-Strain-Upsetting Process Formula Elements

Credits

Other formulas in Rolling Analysis category

How to Evaluate Pressure Considering Rolling Similar to Plane-Strain-Upsetting Process?

FAQs on Pressure Considering Rolling Similar to Plane-Strain-Upsetting Process

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