Shear angle for given area of shear plane, width of cut and uncut chip thickness Calculator

✖Cutting Width can be defined as the width the tool cuts into the workpiece.ⓘ Cutting Width [w_c]			+10% -10%
✖Uncut chip thickness in machining can be referred as the thickness of the undeformed chip.ⓘ Uncut Chip Thickness in Machining [t₁]			+10% -10%
✖Area of shear plane is defined as the area of that plane along which the chip is formed by shear deformation as the tool is forced into the material.ⓘ Area of Shear Plane [A_s]			+10% -10%

✖Shearing angle between is the inclination of the shear plane with the horizontal axis at machining point.ⓘ Shear angle for given area of shear plane, width of cut and uncut chip thickness [ϕ_.]

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Formula

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Shear angle for given area of shear plane, width of cut and uncut chip thickness

Formula

`"ϕ"_{"."} = asin("w"_{"c"}*"t"_{"1"}/"A"_{"s"})`

Example

`"5.257°"=asin("9.6873mm"*"6.94mm"/"733.764mm²")`

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Shear angle for given area of shear plane, width of cut and uncut chip thickness Solution

STEP 0: Pre-Calculation Summary

Formula Used

Shearing Angle = asin(Cutting Width*Uncut Chip Thickness in Machining/Area of Shear Plane)
ϕ_. = asin(w_c*t₁/A_s)
This formula uses 2 Functions, 4 Variables

Functions Used

sin - Sine is a trigonometric function that describes the ratio of the length of the opposite side of a right triangle to the length of the hypotenuse., sin(Angle)
asin - The inverse sine function, is a trigonometric function that takes a ratio of two sides of a right triangle and outputs the angle opposite the side with the given ratio., asin(Number)

Variables Used

Shearing Angle - (Measured in Radian) - Shearing angle between is the inclination of the shear plane with the horizontal axis at machining point.
Cutting Width - (Measured in Meter) - Cutting Width can be defined as the width the tool cuts into the workpiece.
Uncut Chip Thickness in Machining - (Measured in Meter) - Uncut chip thickness in machining can be referred as the thickness of the undeformed chip.
Area of Shear Plane - (Measured in Square Meter) - Area of shear plane is defined as the area of that plane along which the chip is formed by shear deformation as the tool is forced into the material.

STEP 1: Convert Input(s) to Base Unit

Cutting Width: 9.6873 Millimeter --> 0.0096873 Meter (Check conversion here)
Uncut Chip Thickness in Machining: 6.94 Millimeter --> 0.00694 Meter (Check conversion here)
Area of Shear Plane: 733.764 Square Millimeter --> 0.000733764 Square Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

ϕ_. = asin(w_c*t₁/A_s) --> asin(0.0096873*0.00694/0.000733764)

Evaluating ... ...

ϕ_. = 0.0917519569605008

STEP 3: Convert Result to Output's Unit

0.0917519569605008 Radian -->5.25699989590366 Degree (Check conversion here)

FINAL ANSWER

5.25699989590366 ≈ 5.257 Degree <-- Shearing Angle

(Calculation completed in 00.004 seconds)

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Home » Engineering » Production Engineering » Metal Cutting » Merchant Force Circle » Geometry and Dimensions » Shear angle for given area of shear plane, width of cut and uncut chip thickness

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Created by Vinay Mishra

Indian Institute for Aeronautical Engineering and Information Technology (IIAEIT), Pune

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Verified by Rushi Shah

K J Somaiya College of Engineering (K J Somaiya), Mumbai

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< 8 Geometry and Dimensions Calculators

Uncut chip thickness given cutting force, shear stress, cut, friction, normal rake and shear angles

Go Uncut Chip Thickness in Machining = Cutting Force in Metal Cutting*(cos(Shearing Angle+Cutting Friction Angle-Rake Angle of Cutting Tool))/(Cutting Width*Average Shear Stress Produced on Shear Plane*cos(Cutting Friction Angle-Rake Angle of Cutting Tool))

Width of cut given cutting force, shear stress, uncut chip, friction, normal rake and shear angles

Go Cutting Width = Cutting Force in Metal Cutting*(cos(Shearing Angle+Cutting Friction Angle-Rake Angle of Cutting Tool))/(Average Shear Stress Produced on Shear Plane*Uncut Chip Thickness in Machining*cos(Cutting Friction Angle-Rake Angle of Cutting Tool))

Area of shear plane for given shear angle, width of cut and uncut chip thickness

Go Area of Shear Plane = (Uncut Chip Thickness in Machining*Cutting Width)/sin(Shearing Angle)

Uncut chip thickness for given width of cut, shear angle and area of shear plane

Go Uncut Chip Thickness in Machining = (Area of Shear Plane*sin(Shearing Angle))/Cutting Width

Width of cut for given shear angle, uncut chip thickness and area of shear plane

Go Cutting Width = (Area of Shear Plane*sin(Shearing Angle))/Uncut Chip Thickness in Machining

Shear angle for given area of shear plane, width of cut and uncut chip thickness

Go Shearing Angle = asin(Cutting Width*Uncut Chip Thickness in Machining/Area of Shear Plane)

Side cutting edge angle for given width of cut

Go Side Cutting Edge Angle for Metal Cutting = acos(Depth of Cut Provided by Tool/Cutting Width)

Width of cut for given side cutting edge angle

Go Cutting Width = Depth of Cut Provided by Tool/cos(Side Cutting Edge Angle for Metal Cutting)

Shear angle for given area of shear plane, width of cut and uncut chip thickness Formula

Shearing Angle = asin(Cutting Width*Uncut Chip Thickness in Machining/Area of Shear Plane)
ϕ_. = asin(w_c*t₁/A_s)

What is the significance of the shear angle?

The shear angle is of fundamental importance in chip formation. The smaller the shear angle, the larger the strain, the machining forces, and the power requirements. A higher shear plane angle means a smaller shear plane, which means lower shear force, cutting forces, power, and temperature.

How to Calculate Shear angle for given area of shear plane, width of cut and uncut chip thickness?

Shear angle for given area of shear plane, width of cut and uncut chip thickness calculator uses Shearing Angle = asin(Cutting Width*Uncut Chip Thickness in Machining/Area of Shear Plane) to calculate the Shearing Angle, Shear angle for given area of shear plane, width of cut and uncut chip thickness is defined as an angle between the shear plane and the horizontal plane. Shearing Angle is denoted by ϕ_. symbol.

How to calculate Shear angle for given area of shear plane, width of cut and uncut chip thickness using this online calculator? To use this online calculator for Shear angle for given area of shear plane, width of cut and uncut chip thickness, enter Cutting Width (w_c), Uncut Chip Thickness in Machining (t₁) & Area of Shear Plane (A_s) and hit the calculate button. Here is how the Shear angle for given area of shear plane, width of cut and uncut chip thickness calculation can be explained with given input values -> 288.3506 = asin(0.0096873*0.00694/0.000733764).

FAQ

What is Shear angle for given area of shear plane, width of cut and uncut chip thickness?

Shear angle for given area of shear plane, width of cut and uncut chip thickness is defined as an angle between the shear plane and the horizontal plane and is represented as ϕ_. = asin(w_c*t₁/A_s) or Shearing Angle = asin(Cutting Width*Uncut Chip Thickness in Machining/Area of Shear Plane). Cutting Width can be defined as the width the tool cuts into the workpiece, Uncut chip thickness in machining can be referred as the thickness of the undeformed chip & Area of shear plane is defined as the area of that plane along which the chip is formed by shear deformation as the tool is forced into the material.

How to calculate Shear angle for given area of shear plane, width of cut and uncut chip thickness?

Shear angle for given area of shear plane, width of cut and uncut chip thickness is defined as an angle between the shear plane and the horizontal plane is calculated using Shearing Angle = asin(Cutting Width*Uncut Chip Thickness in Machining/Area of Shear Plane). To calculate Shear angle for given area of shear plane, width of cut and uncut chip thickness, you need Cutting Width (w_c), Uncut Chip Thickness in Machining (t₁) & Area of Shear Plane (A_s). With our tool, you need to enter the respective value for Cutting Width, Uncut Chip Thickness in Machining & Area of Shear Plane 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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