Initial Stock Thickness given Pressure on Rolls Calculator

✖The Mean Yield Shear Stress of Work Material represents the average shear stress at which the material begins to yield or undergo plastic deformation.ⓘ Mean Yield Shear Stress of Work Material [S]			+10% -10%
✖Thickness at given Point is defined as the thickness of stock at any point between entry and neutral point.ⓘ Thickness at given Point [h_s]			+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_friction]			+10% -10%
✖Factor H at Entry Point on Workpiece is a factor calculated using radius of rolls, thickness of work, bite angle.ⓘ Factor H at Entry Point on Workpiece [H_i]			+10% -10%
✖Factor H in Rolling Calculation is a factor calculated using radius of rolls, thickness of work and position of that point.ⓘ Factor H in Rolling Calculation [H_r]			+10% -10%
✖The Pressure Acting on Rolls is the force per unit area of Rollers/plates.ⓘ Pressure Acting on Rolls [P]			+10% -10%

✖Initial Stock Thickness is the thickness of sheet before rolling operation.ⓘ Initial Stock Thickness given Pressure on Rolls [h_t]

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Formula

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Initial Stock Thickness given Pressure on Rolls

Formula

`"h"_{"t"} = ("S"*"h"_{"s"}*exp("μ"_{"friction"}*("H"_{"i"}-"H"_{"r"})))/"P"`

Example

`"2.745823mm"=("58730"*"0.00313577819561353mm"*exp("0.4"*("3.36"-"0.77")))/"0.000189N/mm²"`

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Initial Stock Thickness given Pressure on Rolls Solution

STEP 0: Pre-Calculation Summary

Formula Used

Initial Stock Thickness = (Mean Yield Shear Stress of Work Material*Thickness at given Point*exp(Friction Coefficient*(Factor H at Entry Point on Workpiece-Factor H in Rolling Calculation)))/Pressure Acting on Rolls
h_t = (S*h_s*exp(μ_friction*(H_i-H_r)))/P
This formula uses 1 Functions, 7 Variables

Functions Used

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)

Variables Used

Initial Stock Thickness - (Measured in Meter) - Initial Stock Thickness is the thickness of sheet before rolling operation.
Mean Yield Shear Stress of Work Material - The Mean Yield Shear Stress of Work Material represents the average shear stress at which the material begins to yield or undergo plastic deformation.
Thickness at given Point - (Measured in Meter) - Thickness at given Point is defined as the thickness of stock at any point between entry and neutral point.
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.
Factor H at Entry Point on Workpiece - Factor H at Entry Point on Workpiece is a factor calculated using radius of rolls, thickness of work, bite angle.
Factor H in Rolling Calculation - Factor H in Rolling Calculation is a factor calculated using radius of rolls, thickness of work and position of that point.
Pressure Acting on Rolls - (Measured in Pascal) - The Pressure Acting on Rolls is the force per unit area of Rollers/plates.

STEP 1: Convert Input(s) to Base Unit

Mean Yield Shear Stress of Work Material: 58730 --> No Conversion Required
Thickness at given Point: 0.00313577819561353 Millimeter --> 3.13577819561353E-06 Meter (Check conversion here)
Friction Coefficient: 0.4 --> No Conversion Required
Factor H at Entry Point on Workpiece: 3.36 --> No Conversion Required
Factor H in Rolling Calculation: 0.77 --> No Conversion Required
Pressure Acting on Rolls: 0.000189 Newton per Square Millimeter --> 189 Pascal (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

h_t = (S*h_s*exp(μ_friction*(H_i-H_r)))/P --> (58730*3.13577819561353E-06*exp(0.4*(3.36-0.77)))/189

Evaluating ... ...

h_t = 0.00274582348915817

STEP 3: Convert Result to Output's Unit

0.00274582348915817 Meter -->2.74582348915817 Millimeter (Check conversion here)

FINAL ANSWER

2.74582348915817 ≈ 2.745823 Millimeter <-- Initial Stock Thickness

(Calculation completed in 00.004 seconds)

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Created by Rajat Vishwakarma

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*(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 given 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)/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

Bite Angle

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

Maximum Reduction in Thickness Possible

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

Projected Length

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

Initial Stock Thickness given Pressure on Rolls 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 Initial Stock Thickness given Pressure on Rolls?

Initial Stock Thickness given Pressure on Rolls calculator uses Initial Stock Thickness = (Mean Yield Shear Stress of Work Material*Thickness at given Point*exp(Friction Coefficient*(Factor H at Entry Point on Workpiece-Factor H in Rolling Calculation)))/Pressure Acting on Rolls to calculate the Initial Stock Thickness, The Initial stock thickness given pressure on rolls formula is the initial thickness of the workpiece before rolling. Initial Stock Thickness is denoted by h_t symbol.

How to calculate Initial Stock Thickness given Pressure on Rolls using this online calculator? To use this online calculator for Initial Stock Thickness given Pressure on Rolls, enter Mean Yield Shear Stress of Work Material (S), Thickness at given Point (h_s), Friction Coefficient (μ_friction), Factor H at Entry Point on Workpiece (H_i), Factor H in Rolling Calculation (H_r) & Pressure Acting on Rolls (P) and hit the calculate button. Here is how the Initial Stock Thickness given Pressure on Rolls calculation can be explained with given input values -> 2745.823 = (58730*3.13577819561353E-06*exp(0.4*(3.36-0.77)))/189.

FAQ

What is Initial Stock Thickness given Pressure on Rolls?

The Initial stock thickness given pressure on rolls formula is the initial thickness of the workpiece before rolling and is represented as h_t = (S*h_s*exp(μ_friction*(H_i-H_r)))/P or Initial Stock Thickness = (Mean Yield Shear Stress of Work Material*Thickness at given Point*exp(Friction Coefficient*(Factor H at Entry Point on Workpiece-Factor H in Rolling Calculation)))/Pressure Acting on Rolls. The Mean Yield Shear Stress of Work Material represents the average shear stress at which the material begins to yield or undergo plastic deformation, Thickness at given Point is defined as the thickness of stock at any point between entry and neutral point, 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, Factor H at Entry Point on Workpiece is a factor calculated using radius of rolls, thickness of work, bite angle, Factor H in Rolling Calculation is a factor calculated using radius of rolls, thickness of work and position of that point & The Pressure Acting on Rolls is the force per unit area of Rollers/plates.

How to calculate Initial Stock Thickness given Pressure on Rolls?

The Initial stock thickness given pressure on rolls formula is the initial thickness of the workpiece before rolling is calculated using Initial Stock Thickness = (Mean Yield Shear Stress of Work Material*Thickness at given Point*exp(Friction Coefficient*(Factor H at Entry Point on Workpiece-Factor H in Rolling Calculation)))/Pressure Acting on Rolls. To calculate Initial Stock Thickness given Pressure on Rolls, you need Mean Yield Shear Stress of Work Material (S), Thickness at given Point (h_s), Friction Coefficient (μ_friction), Factor H at Entry Point on Workpiece (H_i), Factor H in Rolling Calculation (H_r) & Pressure Acting on Rolls (P). With our tool, you need to enter the respective value for Mean Yield Shear Stress of Work Material, Thickness at given Point, Friction Coefficient, Factor H at Entry Point on Workpiece, Factor H in Rolling Calculation & Pressure Acting on Rolls 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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