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

STEP 0: Pre-Calculation Summary
Formula Used
Shear angle = asin(Width of cut*Uncut Chip Thickness/Area of shear plane)
ϕ = asin(w*t1/AS)
This formula uses 2 Functions, 4 Variables
Functions Used
sin - Trigonometric sine function, sin(Angle)
asin - Inverse trigonometric sine function, asin(Number)
Variables Used
Shear angle - (Measured in Radian) - Shear angle is the inclination of the shear plane with the horizontal axis at machining point.
Width of cut - (Measured in Meter) - The width of cut is defined as the width the tool cuts into the workpiece.
Uncut Chip Thickness - (Measured in Meter) - Uncut Chip Thickness is 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
Width of cut: 10 Meter --> 10 Meter No Conversion Required
Uncut Chip Thickness: 1.2 Millimeter --> 0.0012 Meter (Check conversion here)
Area of shear plane: 10 Square Meter --> 10 Square Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
ϕ = asin(w*t1/AS) --> asin(10*0.0012/10)
Evaluating ... ...
ϕ = 0.00120000028800019
STEP 3: Convert Result to Output's Unit
0.00120000028800019 Radian -->0.0687549519169069 Degree (Check conversion here)
FINAL ANSWER
0.0687549519169069 Degree <-- Shear angle
(Calculation completed in 00.021 seconds)

Credits

Created by Vinay Mishra
Indian Institute for Aeronautical Engineering and Information Technology (IIAEIT), Pune
Vinay Mishra has created this Calculator and 300+ more calculators!
Verified by Rushi Shah
K J Somaiya College of Engineering (K J Somaiya), Mumbai
Rushi Shah has verified this Calculator and 200+ more calculators!

10+ Merchant Force Circle (Mechanics of Orthogonal metal cutting) Calculators

Coefficient of friction for given thrust force, cutting force and normal rake angle
Coefficient of Friction = (Thrust force+Cutting Force*tan(Normal rake angle))/(Cutting Force-Thrust force*tan(Normal rake angle)) Go
Frictional force along tool rake face for given cutting and thrust forces, normal rake angle
Frictional force on the sleeve = (Cutting Force*(sin(Normal rake angle)))+(Axial Thrust*(cos(Normal rake angle))) Go
Force acting Normal to Rake Face given Cutting Force and Thrust Force
Normal Force = (Cutting Force*cos(Normal rake angle))-(Thrust force*sin(Normal rake angle)) Go
Area of shear plane for given shear angle, width of cut and uncut chip thickness
Area of shear plane = (Uncut Chip Thickness*Width of cut)/sin(Shear angle) Go
Width of cut for given shear angle, uncut chip thickness and area of shear plane
Width of cut = (Area of shear plane*sin(Shear angle))/Uncut Chip Thickness Go
Shear angle for given area of shear plane, width of cut and uncut chip thickness
Shear angle = asin(Width of cut*Uncut Chip Thickness/Area of shear plane) Go
Side cutting edge angle for given width of cut
Side Cutting Edge Angle = acos(Width of cut/Depth of cut) Go
Width of cut for given side cutting edge angle
Width of cut = Depth of Cut/cos(Side Cutting Edge Angle) Go
Coefficient of Friction given Forces Normal and along Tool Rake Face
Coefficient of Friction = Force of Friction/Normal Force Go
Coefficient of friction for given friction angle
Coefficient of Friction = tan(Angle of Friction) Go

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

Shear angle = asin(Width of cut*Uncut Chip Thickness/Area of shear plane)
ϕ = asin(w*t1/AS)

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 Shear angle = asin(Width of cut*Uncut Chip Thickness/Area of shear plane) to calculate the Shear 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. Shear 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 Width of cut (w), Uncut Chip Thickness (t1) & Area of shear plane (AS) 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 -> 0.068755 = asin(10*0.0012/10).

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*t1/AS) or Shear angle = asin(Width of cut*Uncut Chip Thickness/Area of shear plane). The width of cut is defined as the width the tool cuts into the workpiece, Uncut Chip Thickness is 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 Shear angle = asin(Width of cut*Uncut Chip Thickness/Area of shear plane). To calculate Shear angle for given area of shear plane, width of cut and uncut chip thickness, you need Width of cut (w), Uncut Chip Thickness (t1) & Area of shear plane (AS). With our tool, you need to enter the respective value for Width of cut, Uncut Chip Thickness & 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.
How many ways are there to calculate Shear angle?
In this formula, Shear angle uses Width of cut, Uncut Chip Thickness & Area of shear plane. We can use 1 other way(s) to calculate the same, which is/are as follows -
  • Shear angle = Rake Angle-Friction angle+(arccos(Resultant Force/Force along shear plane))
Share Image
Let Others Know
Facebook
Twitter
Reddit
LinkedIn
Email
WhatsApp
Copied!