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Angle Subtended by Neutral Point Formula

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The angle subtended at neutral point refers to the maximum attainable angle between the roll radius at the first contact and the roll centers during rolling of metals. Check FAQs

φ n = \sqrt{\frac{h fi}{R}} \cdot \tan (\frac{H n}{2} \cdot \sqrt{\frac{h fi}{R}})

φ_n - Angle subtended at Neutral Point?h_fi - Thickness after Rolling?R - Roller Radius?H_n - Factor H at Neutral Point?

Angle Subtended by Neutral Point Example

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Here is how the Angle Subtended by Neutral Point equation looks like with Values.

Here is how the Angle Subtended by Neutral Point equation looks like with Units.

Here is how the Angle Subtended by Neutral Point equation looks like.

5.5182 = \sqrt{\frac{7.2}{102}} \cdot \tan (\frac{2.6179}{2} \cdot \sqrt{\frac{7.2}{102}})

5.5182° = \sqrt{\frac{7.2mm}{102mm}} \cdot \tan (\frac{2.6179}{2} \cdot \sqrt{\frac{7.2mm}{102mm}})

5.5182 = \sqrt{\frac{7.2}{102}} \cdot \tan (\frac{2.6179}{2} \cdot \sqrt{\frac{7.2}{102}})

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Angle Subtended by Neutral Point Solution

Follow our step by step solution on how to calculate Angle Subtended by Neutral Point?

FIRST Step Consider the formula

φ n = \sqrt{\frac{h fi}{R}} \cdot \tan (\frac{H n}{2} \cdot \sqrt{\frac{h fi}{R}})

Next Step Substitute values of Variables

∴

φ n = \sqrt{\frac{7.2mm}{102mm}} \cdot \tan (\frac{2.6179}{2} \cdot \sqrt{\frac{7.2mm}{102mm}})

Next Step Convert Units

∴

φ n = \sqrt{\frac{0.0072m}{0.102m}} \cdot \tan (\frac{2.6179}{2} \cdot \sqrt{\frac{0.0072m}{0.102m}})

Next Step Prepare to Evaluate

∴

φ n = \sqrt{\frac{0.0072}{0.102}} \cdot \tan (\frac{2.6179}{2} \cdot \sqrt{\frac{0.0072}{0.102}})

Next Step Evaluate

∴

φ n = 0.0963101084825006rad

Next Step Convert to Output's Unit

∴

φ n = 5.51816274049543°

LAST Step Rounding Answer

∴

φ n = 5.5182°

Angle Subtended by Neutral Point Formula Elements

Variables

Functions

Angle subtended at Neutral Point

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

Symbol: φ_n

Measurement: AngleUnit: °

Note: Value can be positive or negative.

Formulas to find Angle subtended at Neutral Point

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.

Formulas to find Thickness after Rolling

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.

Formulas to find Roller Radius

Factor H at Neutral Point

Factor H at Neutral Point is used in rolling calculations to account for the interaction between the material, the rollers, and the deformation process.

Symbol: H_n

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Factor H at Neutral Point

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.

Syntax: 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.

Syntax: sqrt(Number)

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

Go Projected Length

L = {(R \cdot Δt)}^{0.5}

Go Factor H at Neutral Point

H n = \frac{H i - \frac{\ln (\frac{h i}{h fi})}{μ f}}{2}

How to Evaluate Angle Subtended by Neutral Point?

Angle Subtended by Neutral Point evaluator 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 evaluate 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 evaluate Angle Subtended by Neutral Point using this online evaluator? To use this online evaluator 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.

FAQs on Angle Subtended by Neutral Point

What is the formula to find Angle Subtended by Neutral Point?

The formula of Angle Subtended by Neutral Point is expressed as Angle subtended at Neutral Point = sqrt(Thickness after Rolling/Roller Radius)*tan(Factor H at Neutral Point/2*sqrt(Thickness after Rolling/Roller Radius)). Here is an example- 316.1674 = sqrt(0.0072/0.102)*tan(2.617882/2*sqrt(0.0072/0.102)).

How to calculate Angle Subtended by Neutral Point?

With Thickness after Rolling (h_fi), Roller Radius (R) & Factor H at Neutral Point (H_n) we can find Angle Subtended by Neutral Point using the 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)). This formula also uses Tangent (tan), Square Root (sqrt) function(s).

Can the Angle Subtended by Neutral Point be negative?

Yes, the Angle Subtended by Neutral Point, measured in Angle can be negative.

Which unit is used to measure Angle Subtended by Neutral Point?

Angle Subtended by Neutral Point is usually measured using the Degree[°] for Angle. Radian[°], Minute[°], Second[°] are the few other units in which Angle Subtended by Neutral Point can be measured.

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