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

✖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.ⓘ Strip Width of Spiral Spring [b]			+10% -10%
✖Flow Stress of Work Material refers to the instantaneous value of stress required to continue deforming a material, effectively keeping the metal flowing.ⓘ Flow Stress of Work Material [σ]			+10% -10%
✖Frictional Shear Factor is generated by the interaction between the workpiece and rolls. It contributes to the overall deformation of the material.ⓘ Frictional Shear Factor [μ_sf]			+10% -10%
✖The Roller Radius is the distance between the center and the point on the circumference of the roller.ⓘ Roller Radius [R]			+10% -10%
✖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.ⓘ Bite Angle [α_b]			+10% -10%
✖Thickness before Rolling is the thickness of sheet before rolling operation begins.ⓘ Thickness before Rolling [h_i]			+10% -10%
✖Thickness after Rolling is the final thickness of the workpiece after the rolling process.ⓘ Thickness after Rolling [h_fi]			+10% -10%

✖Pressure Acting while Rolling is the force per unit area of Rollers/plates during the rolling process.ⓘ Pressure Considering Rolling Similar to Plane-Strain-Upsetting Process [P_r]

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Pressure Considering Rolling Similar to Plane-Strain-Upsetting Process

Formula

`"P"_{"r"} = "b"*(2*"σ")/sqrt(3)*(1+("μ"_{"sf"}*"R"*pi/180*"α"_{"b"})/(2*("h"_{"i"}+"h"_{"fi"})))*"R"*pi/180*"α"_{"b"}`

Example

`"3.3E^-5N/mm²"="14.5mm"*(2*"2.1N/mm²")/sqrt(3)*(1+("0.41"*"102mm"*pi/180*"30.00°")/(2*("3.4mm"+"7.2mm")))*"102mm"*pi/180*"30.00°"`

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

STEP 0: Pre-Calculation Summary

Formula Used

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
P_r = b*(2*σ)/sqrt(3)*(1+(μ_sf*R*pi/180*α_b)/(2*(h_i+h_fi)))*R*pi/180*α_b
This formula uses 1 Constants, 1 Functions, 8 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

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 while Rolling - (Measured in Pascal) - Pressure Acting while Rolling is the force per unit area of Rollers/plates during the rolling process.
Strip Width of Spiral Spring - (Measured in Meter) - 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.
Flow Stress of Work Material - (Measured in Pascal) - Flow Stress of Work Material refers to the instantaneous value of stress required to continue deforming a material, effectively keeping the metal flowing.
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.
Roller Radius - (Measured in Meter) - The Roller Radius is the distance between the center and the point on the circumference of the roller.
Bite Angle - (Measured in Radian) - 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.
Thickness before Rolling - (Measured in Meter) - Thickness before Rolling is the thickness of sheet before rolling operation begins.
Thickness after Rolling - (Measured in Meter) - Thickness after Rolling is the final thickness of the workpiece after the rolling process.

STEP 1: Convert Input(s) to Base Unit

Strip Width of Spiral Spring: 14.5 Millimeter --> 0.0145 Meter (Check conversion here)
Flow Stress of Work Material: 2.1 Newton per Square Millimeter --> 2100000 Pascal (Check conversion here)
Frictional Shear Factor: 0.41 --> No Conversion Required
Roller Radius: 102 Millimeter --> 0.102 Meter (Check conversion here)
Bite Angle: 30 Degree --> 0.5235987755982 Radian (Check conversion here)
Thickness before Rolling: 3.4 Millimeter --> 0.0034 Meter (Check conversion here)
Thickness after Rolling: 7.2 Millimeter --> 0.0072 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

P_r = b*(2*σ)/sqrt(3)*(1+(μ_sf*R*pi/180*α_b)/(2*(h_i+h_fi)))*R*pi/180*α_b --> 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

Evaluating ... ...

P_r = 33.3650773318261

STEP 3: Convert Result to Output's Unit

33.3650773318261 Pascal -->3.33650773318261E-05 Newton per Square Millimeter (Check conversion here)

FINAL ANSWER

3.33650773318261E-05 ≈ 3.3E-5 Newton per Square Millimeter <-- Pressure Acting while Rolling

(Calculation completed in 00.036 seconds)

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

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Pressure Considering Rolling Similar to Plane-Strain-Upsetting Process

Go 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

Initial Stock Thickness given Pressure on Rolls

Go Initial Stock Thickness = (Mean Yield Shear Stress of Work Material*Thickness at given Point*exp(Friction Coefficient in Rolling Analysis*(Factor H at Entry Point on Workpiece-Factor H in Rolling Calculation)))/Pressure Acting on Rolls

Factor H used in Rolling Calculations

Go Factor H in Rolling Calculation = 2*sqrt(Roller Radius/Thickness after Rolling)*atan(sqrt(Roller Radius/Thickness after Rolling))*Angle made by Point Roll Center and Normal

Angle Subtended by Neutral Point

Go Angle subtended at Neutral Point = sqrt(Thickness after Rolling/Roller Radius)*tan(Factor H at Neutral Point/2*sqrt(Thickness after Rolling/Roller Radius))

Factor H at Neutral Point

Go Factor H at Neutral Point = (Factor H at Entry Point on Workpiece-ln(Thickness before Rolling/Thickness after Rolling)/Friction Coefficient in Rolling Analysis)/2

Total Elongation of Stock

Go Total Stock or Workpiece Elongation = Initial Cross Sectional Area/Final Cross Sectional Area

Projected Area

Go Projected Area = Width*(Roller Radius*Change in Thickness)^0.5

Maximum Reduction in Thickness Possible

Go Change in Thickness = Friction Coefficient in Rolling Analysis^2*Roller Radius

Bite Angle

Go Bite Angle = acos(1-Height/(2*Roller Radius))

Projected Length

Go Projected Length = (Roller Radius*Change in Thickness)^0.5

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

Pressure Considering Rolling Similar to Plane-Strain-Upsetting Process calculator 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 calculate 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 calculate Pressure Considering Rolling Similar to Plane-Strain-Upsetting Process using this online calculator? To use this online calculator 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. Here is how the Pressure Considering Rolling Similar to Plane-Strain-Upsetting Process calculation can be explained with given input values -> 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.

FAQ

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

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 and is represented as P_r = b*(2*σ)/sqrt(3)*(1+(μ_sf*R*pi/180*α_b)/(2*(h_i+h_fi)))*R*pi/180*α_b or 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. 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, Flow Stress of Work Material refers to the instantaneous value of stress required to continue deforming a material, effectively keeping the metal flowing, Frictional Shear Factor is generated by the interaction between the workpiece and rolls. It contributes to the overall deformation of the material, The Roller Radius is the distance between the center and the point on the circumference of the roller, 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, Thickness before Rolling is the thickness of sheet before rolling operation begins & Thickness after Rolling is the final thickness of the workpiece after the rolling process.

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

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 is calculated using 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 calculate Pressure Considering Rolling Similar to Plane-Strain-Upsetting Process, you need 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). With our tool, you need to enter the respective value for Strip Width of Spiral Spring, Flow Stress of Work Material, Frictional Shear Factor, Roller Radius, Bite Angle, Thickness before Rolling & Thickness after Rolling 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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