Angle Subtended by Neutral Point Calculator

✖Thickness after Rolling is the thickness of the workpiece after rolling and is denoted by the symbol h.ⓘ Thickness after Rolling [h_fi]			+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%
✖Factor H at Neutral Point is its value where the pressure is at its peak.ⓘ Factor H at Neutral Point [H_n]			+10% -10%

✖Angle subtended at Neutral Point defines the position of neutral point with respect to line joining the two centers of rollers.ⓘ Angle Subtended by Neutral Point [φ_N]

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Formula

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Angle Subtended by Neutral Point

Formula

`"φ"_{"N"} = sqrt("h"_{"fi"}/"R")*tan("H"_{"n"}/2*sqrt("h"_{"fi"}/"R"))`

Example

`"5.518163°"=sqrt("7.2mm"/"102mm")*tan("2.617882"/2*sqrt("7.2mm"/"102mm"))`

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Angle Subtended by Neutral Point Solution

STEP 0: Pre-Calculation Summary

Formula Used

Angle subtended at Neutral Point = sqrt(Thickness after Rolling/Roller Radius)*tan(Factor H at Neutral Point/2*sqrt(Thickness after Rolling/Roller Radius))
φ_N = sqrt(h_fi/R)*tan(H_n/2*sqrt(h_fi/R))
This formula uses 2 Functions, 4 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)
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

Angle subtended at Neutral Point - (Measured in Radian) - Angle subtended at Neutral Point defines the position of neutral point with respect to line joining the two centers of rollers.
Thickness after Rolling - (Measured in Meter) - Thickness after Rolling is the thickness of the workpiece after rolling and is denoted by the symbol h.
Roller Radius - (Measured in Meter) - The Roller Radius is the distance between the center and the point on the circumference of the roller.
Factor H at Neutral Point - Factor H at Neutral Point is its value where the pressure is at its peak.

STEP 1: Convert Input(s) to Base Unit

Thickness after Rolling: 7.2 Millimeter --> 0.0072 Meter (Check conversion here)
Roller Radius: 102 Millimeter --> 0.102 Meter (Check conversion here)
Factor H at Neutral Point: 2.617882 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

φ_N = sqrt(h_fi/R)*tan(H_n/2*sqrt(h_fi/R)) --> sqrt(0.0072/0.102)*tan(2.617882/2*sqrt(0.0072/0.102))

Evaluating ... ...

φ_N = 0.0963101084825006

STEP 3: Convert Result to Output's Unit

0.0963101084825006 Radian -->5.51816274049543 Degree (Check conversion here)

FINAL ANSWER

5.51816274049543 ≈ 5.518163 Degree <-- Angle subtended at Neutral Point

(Calculation completed in 00.008 seconds)

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

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< 10+ Rolling Analysis Calculators

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

Angle Subtended by Neutral Point Formula

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

What is Neutral point?

Neutral point is that point where there is no slip between the work piece and the rolls and frictional forces between material and rollers are in equilibrium. To identify the neutral plane position, the two expressions for the roll pressure p– and p+ should be equated as the pressures from both ends peak at the neutral plane. As at entry the material is pulled in and roller is moving faster than material, but at exit material is pulled back and roller is moving slower than material.

How to Calculate Angle Subtended by Neutral Point?

Angle Subtended by Neutral Point calculator uses Angle subtended at Neutral Point = sqrt(Thickness after Rolling/Roller Radius)*tan(Factor H at Neutral Point/2*sqrt(Thickness after Rolling/Roller Radius)) to calculate the Angle subtended at Neutral Point, The Angle subtended by Neutral point formula is defined as the angle made by neutral point and line joining two roller centers. Angle subtended at Neutral Point is denoted by φ_N symbol.

How to calculate Angle Subtended by Neutral Point using this online calculator? To use this online calculator for Angle Subtended by Neutral Point, enter Thickness after Rolling (h_fi), Roller Radius (R) & Factor H at Neutral Point (H_n) and hit the calculate button. Here is how the Angle Subtended by Neutral Point calculation can be explained with given input values -> 407.8617 = sqrt(0.0072/0.102)*tan(2.617882/2*sqrt(0.0072/0.102)).

FAQ

What is Angle Subtended by Neutral Point?

The Angle subtended by Neutral point formula is defined as the angle made by neutral point and line joining two roller centers and is represented as φ_N = sqrt(h_fi/R)*tan(H_n/2*sqrt(h_fi/R)) or Angle subtended at Neutral Point = sqrt(Thickness after Rolling/Roller Radius)*tan(Factor H at Neutral Point/2*sqrt(Thickness after Rolling/Roller Radius)). Thickness after Rolling is the thickness of the workpiece after rolling and is denoted by the symbol h, The Roller Radius is the distance between the center and the point on the circumference of the roller & Factor H at Neutral Point is its value where the pressure is at its peak.

How to calculate Angle Subtended by Neutral Point?

The Angle subtended by Neutral point formula is defined as the angle made by neutral point and line joining two roller centers is calculated using Angle subtended at Neutral Point = sqrt(Thickness after Rolling/Roller Radius)*tan(Factor H at Neutral Point/2*sqrt(Thickness after Rolling/Roller Radius)). To calculate Angle Subtended by Neutral Point, you need Thickness after Rolling (h_fi), Roller Radius (R) & Factor H at Neutral Point (H_n). With our tool, you need to enter the respective value for Thickness after Rolling, Roller Radius & Factor H at Neutral Point 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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