Shear stress given cutting force, cut size, uncut chip thickness, friction, rake and shear angles Calculator

✖Cutting force on workpiece is the force in the direction of cutting, the same direction as the cutting speed.ⓘ Cutting Force on Workpiece [F'_c]			+10% -10%
✖Shear angle for metal cutting is the inclination of the shear plane with the horizontal axis at machining point.ⓘ Shear Angle for Metal Cutting [ϕ^']			+10% -10%
✖Machining friction angle is termed as the angle between the tool and chip, which resists the flow of the chip along the rake face of the tool.ⓘ Machining Friction Angle [β^']			+10% -10%
✖Cutting tool rake angle is the angle of orientation of tool’s rake surface from the reference plane and measured on machine longitudinal plane.ⓘ Cutting Tool Rake Angle [α^']			+10% -10%
✖Cutting thickness is referred as the thickness at which the tool cuts into the workpiece.ⓘ Cutting Thickness [w_cut]			+10% -10%
✖Uncut chip width is the thickness of the undeformed chip.ⓘ Uncut Chip Width [t₁]			+10% -10%

✖Average Shear Stress Induced on shear plane is the reaction of workpiece when applied to different cutting forces on an imaginary shear plane.ⓘ Shear stress given cutting force, cut size, uncut chip thickness, friction, rake and shear angles [τ_s]

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Shear stress given cutting force, cut size, uncut chip thickness, friction, rake and shear angles

Formula

`"τ"_{"s"} = "F'"_{"c"}*(cos("ϕ"^{"'"}+"β"^{"'"}-"α"^{"'"}))/(("w"_{"cut"}*"t"_{"1"})*cos("β"^{"'"}-"α"^{"'"}))`

Example

`"0.37882MPa"="150N"*(cos("27.3°"+"36.695°"-"8.6215°"))/(("15mm"*"17mm")*cos("36.695°"-"8.6215°"))`

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Shear stress given cutting force, cut size, uncut chip thickness, friction, rake and shear angles Solution

STEP 0: Pre-Calculation Summary

Formula Used

Average Shear Stress Induced on Shear Plane = Cutting Force on Workpiece*(cos(Shear Angle for Metal Cutting+Machining Friction Angle-Cutting Tool Rake Angle))/((Cutting Thickness*Uncut Chip Width)*cos(Machining Friction Angle-Cutting Tool Rake Angle))
τ_s = F'_c*(cos(ϕ^'+β^'-α^'))/((w_cut*t₁)*cos(β^'-α^'))
This formula uses 1 Functions, 7 Variables

Functions Used

cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., cos(Angle)

Variables Used

Average Shear Stress Induced on Shear Plane - (Measured in Pascal) - Average Shear Stress Induced on shear plane is the reaction of workpiece when applied to different cutting forces on an imaginary shear plane.
Cutting Force on Workpiece - (Measured in Newton) - Cutting force on workpiece is the force in the direction of cutting, the same direction as the cutting speed.
Shear Angle for Metal Cutting - (Measured in Radian) - Shear angle for metal cutting is the inclination of the shear plane with the horizontal axis at machining point.
Machining Friction Angle - (Measured in Radian) - Machining friction angle is termed as the angle between the tool and chip, which resists the flow of the chip along the rake face of the tool.
Cutting Tool Rake Angle - (Measured in Radian) - Cutting tool rake angle is the angle of orientation of tool’s rake surface from the reference plane and measured on machine longitudinal plane.
Cutting Thickness - (Measured in Meter) - Cutting thickness is referred as the thickness at which the tool cuts into the workpiece.
Uncut Chip Width - (Measured in Meter) - Uncut chip width is the thickness of the undeformed chip.

STEP 1: Convert Input(s) to Base Unit

Cutting Force on Workpiece: 150 Newton --> 150 Newton No Conversion Required
Shear Angle for Metal Cutting: 27.3 Degree --> 0.476474885794362 Radian (Check conversion here)
Machining Friction Angle: 36.695 Degree --> 0.640448569019199 Radian (Check conversion here)
Cutting Tool Rake Angle: 8.6215 Degree --> 0.150473561460663 Radian (Check conversion here)
Cutting Thickness: 15 Millimeter --> 0.015 Meter (Check conversion here)
Uncut Chip Width: 17 Millimeter --> 0.017 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

τ_s = F'_c*(cos(ϕ^'+β^'-α^'))/((w_cut*t₁)*cos(β^'-α^')) --> 150*(cos(0.476474885794362+0.640448569019199-0.150473561460663))/((0.015*0.017)*cos(0.640448569019199-0.150473561460663))

Evaluating ... ...

τ_s = 378819.835647425

STEP 3: Convert Result to Output's Unit

378819.835647425 Pascal -->0.378819835647424 Megapascal (Check conversion here)

FINAL ANSWER

0.378819835647424 ≈ 0.37882 Megapascal <-- Average Shear Stress Induced on Shear Plane

(Calculation completed in 00.004 seconds)

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Home » Engineering » Production Engineering » Metal Cutting » Merchant Force Circle » Resultants and Stress » Shear stress given cutting force, cut size, uncut chip thickness, friction, rake and shear angles

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Created by Shikha Maurya

Indian Institute of Technology (IIT), Bombay

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

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< 6 Resultants and Stress Calculators

Shear stress given cutting force, cut size, uncut chip thickness, friction, rake and shear angles

Go Average Shear Stress Induced on Shear Plane = Cutting Force on Workpiece*(cos(Shear Angle for Metal Cutting+Machining Friction Angle-Cutting Tool Rake Angle))/((Cutting Thickness*Uncut Chip Width)*cos(Machining Friction Angle-Cutting Tool Rake Angle))

Force acting Normal to Rake Face given Cutting Force and Thrust Force

Go Normal Force Induced on Workpiece = (Cutting Force on Workpiece*cos(Normal Rake Angle of Cutting Tool))-(Thrust Force in Metal Cutting*sin(Normal Rake Angle of Cutting Tool))

Normal rake angle for given Resultant force, force along shear, shear, and friction angle

Go Cutting Tool Rake Angle = Shear Angle for Metal Cutting+Machining Friction Angle-(arccos(Force Produced Along Shear Plane/Resultant Force on Workpiece))

R in merchant circle for given force along shear force, shear, friction and normal rake angles

Go Resultant Force on Workpiece = (Force Produced Along Shear Plane)*(sec(Shear Angle for Metal Cutting+Machining Friction Angle-Cutting Tool Rake Angle))

Resultant force in merchant circle for given cutting force, friction and normal rake angles

Go Resultant Force on Workpiece = Cutting Force on Workpiece*(sec(Machining Friction Angle-Cutting Tool Rake Angle))

Mean normal stress in shear plane for given normal force and shear area

Go Normal Stress on Workpiece = Normal Force Induced on Workpiece/Shear Area on Workpiece

Shear stress given cutting force, cut size, uncut chip thickness, friction, rake and shear angles Formula

What is average shear stress on the shear plane

The average shear stress on the shear plane is the ratio of shear force acting on the shear plane to the average area of the shear plane. The Shear plane is the plane of separation of work material layer in the form of the chip from the parent body due to shear along that plane.

How to Calculate Shear stress given cutting force, cut size, uncut chip thickness, friction, rake and shear angles?

Shear stress given cutting force, cut size, uncut chip thickness, friction, rake and shear angles calculator uses Average Shear Stress Induced on Shear Plane = Cutting Force on Workpiece*(cos(Shear Angle for Metal Cutting+Machining Friction Angle-Cutting Tool Rake Angle))/((Cutting Thickness*Uncut Chip Width)*cos(Machining Friction Angle-Cutting Tool Rake Angle)) to calculate the Average Shear Stress Induced on Shear Plane, The Shear stress given cutting force, cut size, uncut chip thickness, friction, rake and shear angles formula is defined as cutting force multiplied by the cosine of summation of shear angle to the difference of friction and rake angles divided by the product of the uncut chip thickness, width of cut and cosine of difference of friction and rake angles. Average Shear Stress Induced on Shear Plane is denoted by τ_s symbol.

How to calculate Shear stress given cutting force, cut size, uncut chip thickness, friction, rake and shear angles using this online calculator? To use this online calculator for Shear stress given cutting force, cut size, uncut chip thickness, friction, rake and shear angles, enter Cutting Force on Workpiece (F'_c), Shear Angle for Metal Cutting (ϕ^'), Machining Friction Angle (β^'), Cutting Tool Rake Angle (α^'), Cutting Thickness (w_cut) & Uncut Chip Width (t₁) and hit the calculate button. Here is how the Shear stress given cutting force, cut size, uncut chip thickness, friction, rake and shear angles calculation can be explained with given input values -> 3.8E-7 = 150*(cos(0.476474885794362+0.640448569019199-0.150473561460663))/((0.015*0.017)*cos(0.640448569019199-0.150473561460663)).

FAQ

What is Shear stress given cutting force, cut size, uncut chip thickness, friction, rake and shear angles?

The Shear stress given cutting force, cut size, uncut chip thickness, friction, rake and shear angles formula is defined as cutting force multiplied by the cosine of summation of shear angle to the difference of friction and rake angles divided by the product of the uncut chip thickness, width of cut and cosine of difference of friction and rake angles and is represented as τ_s = F'_c*(cos(ϕ^'+β^'-α^'))/((w_cut*t₁)*cos(β^'-α^')) or Average Shear Stress Induced on Shear Plane = Cutting Force on Workpiece*(cos(Shear Angle for Metal Cutting+Machining Friction Angle-Cutting Tool Rake Angle))/((Cutting Thickness*Uncut Chip Width)*cos(Machining Friction Angle-Cutting Tool Rake Angle)). Cutting force on workpiece is the force in the direction of cutting, the same direction as the cutting speed, Shear angle for metal cutting is the inclination of the shear plane with the horizontal axis at machining point, Machining friction angle is termed as the angle between the tool and chip, which resists the flow of the chip along the rake face of the tool, Cutting tool rake angle is the angle of orientation of tool’s rake surface from the reference plane and measured on machine longitudinal plane, Cutting thickness is referred as the thickness at which the tool cuts into the workpiece & Uncut chip width is the thickness of the undeformed chip.

How to calculate Shear stress given cutting force, cut size, uncut chip thickness, friction, rake and shear angles?

The Shear stress given cutting force, cut size, uncut chip thickness, friction, rake and shear angles formula is defined as cutting force multiplied by the cosine of summation of shear angle to the difference of friction and rake angles divided by the product of the uncut chip thickness, width of cut and cosine of difference of friction and rake angles is calculated using Average Shear Stress Induced on Shear Plane = Cutting Force on Workpiece*(cos(Shear Angle for Metal Cutting+Machining Friction Angle-Cutting Tool Rake Angle))/((Cutting Thickness*Uncut Chip Width)*cos(Machining Friction Angle-Cutting Tool Rake Angle)). To calculate Shear stress given cutting force, cut size, uncut chip thickness, friction, rake and shear angles, you need Cutting Force on Workpiece (F'_c), Shear Angle for Metal Cutting (ϕ^'), Machining Friction Angle (β^'), Cutting Tool Rake Angle (α^'), Cutting Thickness (w_cut) & Uncut Chip Width (t₁). With our tool, you need to enter the respective value for Cutting Force on Workpiece, Shear Angle for Metal Cutting, Machining Friction Angle, Cutting Tool Rake Angle, Cutting Thickness & Uncut Chip Width 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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