Shear Plane Angle Calculator

✖Chip Ratio is the thickness of metal before cutting to the thickness of metal after cutting.ⓘ Chip Ratio [r]			+10% -10%
✖Rake Angle is the angle of orientation of tool’s rake surface from the reference plane and measured on machine longitudinal plane.ⓘ Rake Angle [α]			+10% -10%

✖Shear angle metal is the inclination of the shear plane with the horizontal axis at machining point.ⓘ Shear Plane Angle [ϕ]

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Formula

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Shear Plane Angle

Formula

`"ϕ" = arctan(("r"*cos("α"))/(1-"r"*sin("α")))`

Example

`"22.81089°"=arctan(("0.4"*cos("8.56°"))/(1-"0.4"*sin("8.56°")))`

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Shear Plane Angle Solution

STEP 0: Pre-Calculation Summary

Formula Used

Shear Angle Metal = arctan((Chip Ratio*cos(Rake Angle))/(1-Chip Ratio*sin(Rake Angle)))
ϕ = arctan((r*cos(α))/(1-r*sin(α)))
This formula uses 5 Functions, 3 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)
cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., cos(Angle)
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)
ctan - Cotangent is a trigonometric function that is defined as the ratio of the adjacent side to the opposite side in a right triangle., ctan(Angle)
arctan - Inverse trigonometric functions are usually accompanied by the prefix - arc. Mathematically, we represent arctan or the inverse tangent function as tan-1 x or arctan(x)., arctan(Number)

Variables Used

Shear Angle Metal - (Measured in Radian) - Shear angle metal is the inclination of the shear plane with the horizontal axis at machining point.
Chip Ratio - Chip Ratio is the thickness of metal before cutting to the thickness of metal after cutting.
Rake Angle - (Measured in Radian) - Rake Angle is the angle of orientation of tool’s rake surface from the reference plane and measured on machine longitudinal plane.

STEP 1: Convert Input(s) to Base Unit

Chip Ratio: 0.4 --> No Conversion Required
Rake Angle: 8.56 Degree --> 0.149400183970687 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

ϕ = arctan((r*cos(α))/(1-r*sin(α))) --> arctan((0.4*cos(0.149400183970687))/(1-0.4*sin(0.149400183970687)))

Evaluating ... ...

ϕ = 0.398125174793451

STEP 3: Convert Result to Output's Unit

0.398125174793451 Radian -->22.8108922335772 Degree (Check conversion here)

FINAL ANSWER

22.8108922335772 ≈ 22.81089 Degree <-- Shear Angle Metal

(Calculation completed in 00.004 seconds)

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Home » Engineering » Mechanical » Manufacturing » Metal Cutting » Shear Plane Angle

Credits

Created by Kartikay Pandit

National Institute Of Technology (NIT), Hamirpur

Kartikay Pandit has created this Calculator and 10+ more calculators!

Verified by Saurabh Patil

Shri Govindram Seksaria Institute of Technology and Science (SGSITS ), Indore

Saurabh Patil has verified this Calculator and 25+ more calculators!

< 20 Metal Cutting Calculators

Total Minimum Cost

Go Total Minimum Cost = (Minimum Cost/((Tool Cost/Machine Cost+Tool Changing Time)*(1/Number of Rotation-1))^Number of Rotation)

Shear Plane Angle

Go Shear Angle Metal = arctan((Chip Ratio*cos(Rake Angle))/(1-Chip Ratio*sin(Rake Angle)))

Shear Angle

Go Shear Angle Metal = atan(Width*cos(Theta)/(1-Width*sin(Theta)))

Normal Force

Go Normal Force = Centripetal Force*sin(Theta)+Tangential Force*cos(Theta)

Shear Force

Go Shear Force = Centripetal Force*cos(Theta)-Tangential Force*sin(Theta)

Maximum Production Rate

Go Maximum Production Rate = Cost of metal cutting/(((1/Number of Rotations-1)*Tool Changing Time)^Number of Rotations)

Shear Strain in Machining

Go Shear Strain Machining = tan(Shear Angle Plane-Rake Angle)+cos(Shear Angle Plane)

Shear Strain

Go Shear Strain = tan(Shear Angle Metal)+cot(Shear Angle Metal-Rake Angle)

Bend Allowance

Go Bend Allowance = Subtended Angle in Radians*(Radius+Stretch Factor*Bar Thickness of metal)

Volumetric Removal Rate in electrochemical machining

Go Volumetric Removal Rate = Atomic Weight*Current Value/(Material Density*Valency*96500)

Electro Discharge Machining

Go Electro Discharge Machining = Voltage*(1-e^(-Time/(Resistance*Capacitance)))

Peak to Valley Height

Go Height = Feed/(tan(Angle A)+cot(Angle B))

Extrusion and Wire Drawing

Go Extrusion and Wire Drawing = Stretch factor in Drawing operation*ln(Ratio of Area)

Sheer Yield Strength

Go Shear Yield Strength = Width*Feed*cosec(Shear Angle)

Mass Removal Rate

Go Mass Removal Rate = Weight*Current Magnitude/(Valency*96500)

Specific Power Consumption

Go Specific Power Consumption = Force/(Width*Feed)

Cutting Speed given Angular Speed

Go Cutting Speed = pi*Diameter*Angular Speed

Shear Strain given Tangential Displacement and Original Length

Go Shear Strain = Tangential Displacement/Initial Length

Maximum Profit Rate

Go Maximum Profit Rate = 1/(Feed*Rotation Speed)

Peak to Valley Height given Feed and Radius

Go Peak to Valley Height = (Feed^2)/8*Radius

Shear Plane Angle Formula

Shear Angle Metal = arctan((Chip Ratio*cos(Rake Angle))/(1-Chip Ratio*sin(Rake Angle)))
ϕ = arctan((r*cos(α))/(1-r*sin(α)))

What is Shear Plane?

The shear plane (slipping plane) is an imaginary surface separating the thin layer of liquid bound to the solid surface and showing elastic behavior from the rest of liquid showing normal viscous behavior.

How to Calculate Shear Plane Angle?

Shear Plane Angle calculator uses Shear Angle Metal = arctan((Chip Ratio*cos(Rake Angle))/(1-Chip Ratio*sin(Rake Angle))) to calculate the Shear Angle Metal, The shear plane angle is the angle of inclination of the assumed shear plane from the cutting velocity vector, as measured on orthogonal plane. Shear Angle Metal is denoted by ϕ symbol.

How to calculate Shear Plane Angle using this online calculator? To use this online calculator for Shear Plane Angle, enter Chip Ratio (r) & Rake Angle (α) and hit the calculate button. Here is how the Shear Plane Angle calculation can be explained with given input values -> 1306.968 = arctan((0.4*cos(0.149400183970687))/(1-0.4*sin(0.149400183970687))).

FAQ

What is Shear Plane Angle?

The shear plane angle is the angle of inclination of the assumed shear plane from the cutting velocity vector, as measured on orthogonal plane and is represented as ϕ = arctan((r*cos(α))/(1-r*sin(α))) or Shear Angle Metal = arctan((Chip Ratio*cos(Rake Angle))/(1-Chip Ratio*sin(Rake Angle))). Chip Ratio is the thickness of metal before cutting to the thickness of metal after cutting & Rake Angle is the angle of orientation of tool’s rake surface from the reference plane and measured on machine longitudinal plane.

How to calculate Shear Plane Angle?

The shear plane angle is the angle of inclination of the assumed shear plane from the cutting velocity vector, as measured on orthogonal plane is calculated using Shear Angle Metal = arctan((Chip Ratio*cos(Rake Angle))/(1-Chip Ratio*sin(Rake Angle))). To calculate Shear Plane Angle, you need Chip Ratio (r) & Rake Angle (α). With our tool, you need to enter the respective value for Chip Ratio & Rake Angle 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 Metal?

In this formula, Shear Angle Metal uses Chip Ratio & Rake Angle. We can use 1 other way(s) to calculate the same, which is/are as follows -

Shear Angle Metal = atan(Width*cos(Theta)/(1-Width*sin(Theta)))

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