Shear angle for given Resultant force, force along shear force, friction, and normal rake angles Calculator

✖Rake angle in machining the angle of orientation of tool’s rake surface from the reference plane and measured on machine longitudinal plane.ⓘ Rake Angle in Machining [α_rake]			+10% -10%
✖Friction angle in machining is termed as the angle between the tool and chip, which resists the flow of the chip along the rake face of the tool is friction force.ⓘ Friction Angle in Machining [β_friction]			+10% -10%
✖Force along shear plane in machining is the shear force along the shear plane.ⓘ Force Along Shear Plane in Machining [F_shr]			+10% -10%
✖Resultant force in machining is the vector sum of cutting force and thrust force.ⓘ Resultant Force in Machining [R_o]			+10% -10%

✖Shear angle in machining is the inclination of the shear plane with the horizontal axis at machining point.ⓘ Shear angle for given Resultant force, force along shear force, friction, and normal rake angles [ϕ]

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Shear angle for given Resultant force, force along shear force, friction, and normal rake angles

Formula

`"ϕ" = "α"_{"rake"}-"β"_{"friction"}+(arccos("F"_{"shr"}/"R"_{"o"}))`

Example

`"45.00002°"="33°"-"59°"+(arccos("30.5N"/"93.6825N"))`

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Shear angle for given Resultant force, force along shear force, friction, and normal rake angles Solution

STEP 0: Pre-Calculation Summary

Formula Used

Shear Angle in Machining = Rake Angle in Machining-Friction Angle in Machining+(arccos(Force Along Shear Plane in Machining/Resultant Force in Machining))
ϕ = α_rake-β_friction+(arccos(F_shr/R_o))
This formula uses 2 Functions, 5 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)
arccos - Arccosine function, is the inverse function of the cosine function.It is the function that takes a ratio as an input and returns the angle whose cosine is equal to that ratio., arccos(Number)

Variables Used

Shear Angle in Machining - (Measured in Radian) - Shear angle in machining is the inclination of the shear plane with the horizontal axis at machining point.
Rake Angle in Machining - (Measured in Radian) - Rake angle in machining the angle of orientation of tool’s rake surface from the reference plane and measured on machine longitudinal plane.
Friction Angle in Machining - (Measured in Radian) - Friction angle in machining is termed as the angle between the tool and chip, which resists the flow of the chip along the rake face of the tool is friction force.
Force Along Shear Plane in Machining - (Measured in Newton) - Force along shear plane in machining is the shear force along the shear plane.
Resultant Force in Machining - (Measured in Newton) - Resultant force in machining is the vector sum of cutting force and thrust force.

STEP 1: Convert Input(s) to Base Unit

Rake Angle in Machining: 33 Degree --> 0.57595865315802 Radian (Check conversion here)
Friction Angle in Machining: 59 Degree --> 1.02974425867646 Radian (Check conversion here)
Force Along Shear Plane in Machining: 30.5 Newton --> 30.5 Newton No Conversion Required
Resultant Force in Machining: 93.6825 Newton --> 93.6825 Newton No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

ϕ = α_rake-β_friction+(arccos(F_shr/R_o)) --> 0.57595865315802-1.02974425867646+(arccos(30.5/93.6825))

Evaluating ... ...

ϕ = 0.785398599506867

STEP 3: Convert Result to Output's Unit

0.785398599506867 Radian -->45.0000249872375 Degree (Check conversion here)

FINAL ANSWER

45.0000249872375 ≈ 45.00002 Degree <-- Shear Angle in Machining

(Calculation completed in 00.004 seconds)

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Home » Engineering » Production Engineering » Metal Cutting » Merchant Force Circle » Force Normal to Shear » Shear angle for given Resultant force, force along shear force, friction, and normal rake angles

Credits

Created by Shikha Maurya

Indian Institute of Technology (IIT), Bombay

Shikha Maurya has created this Calculator and 100+ 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!

< 4 Force Normal to Shear Calculators

Force normal to shear force for given cutting force, thrust force, and shear angle

Go Normal Force Induced on Job = (Cutting Force in Machining*(sin(Shear Angle in Machining)))+(Axial Thrust*(cos(Shear Angle in Machining)))

Shear angle for given Resultant force, force along shear force, friction, and normal rake angles

Go Shear Angle in Machining = Rake Angle in Machining-Friction Angle in Machining+(arccos(Force Along Shear Plane in Machining/Resultant Force in Machining))

Cutting Shear Force given Uncut Chip Thickness and Shear Angle

Go Shear Force in Machining = (Shear Stress Induced on Job*Thickness of Cut*Uncut Chip Thickness)/sin(Shear Angle in Machining)

Force normal to shear force for given mean normal shear stress and area of shear plane

Go Normal Force Induced on Job = Shear Stress*Shear Area

Shear angle for given Resultant force, force along shear force, friction, and normal rake angles Formula

Shear Angle in Machining = Rake Angle in Machining-Friction Angle in Machining+(arccos(Force Along Shear Plane in Machining/Resultant Force in Machining))
ϕ = α_rake-β_friction+(arccos(F_shr/R_o))

What is Shear angle

Shear angle is the angle formed between shear force acting on shear plane and the longitudinal plane of the work piece

How to Calculate Shear angle for given Resultant force, force along shear force, friction, and normal rake angles?

Shear angle for given Resultant force, force along shear force, friction, and normal rake angles calculator uses Shear Angle in Machining = Rake Angle in Machining-Friction Angle in Machining+(arccos(Force Along Shear Plane in Machining/Resultant Force in Machining)) to calculate the Shear Angle in Machining, Shear angle for given Resultant force, force along shear force, friction, and normal rake angles is inclination between the shear plane and longitudinal plane. Shear Angle in Machining is denoted by ϕ symbol.

How to calculate Shear angle for given Resultant force, force along shear force, friction, and normal rake angles using this online calculator? To use this online calculator for Shear angle for given Resultant force, force along shear force, friction, and normal rake angles, enter Rake Angle in Machining (α_rake), Friction Angle in Machining (β_friction), Force Along Shear Plane in Machining (F_shr) & Resultant Force in Machining (R_o) and hit the calculate button. Here is how the Shear angle for given Resultant force, force along shear force, friction, and normal rake angles calculation can be explained with given input values -> 5099.326 = 0.57595865315802-1.02974425867646+(arccos(30.5/93.6825)).

FAQ

What is Shear angle for given Resultant force, force along shear force, friction, and normal rake angles?

Shear angle for given Resultant force, force along shear force, friction, and normal rake angles is inclination between the shear plane and longitudinal plane and is represented as ϕ = α_rake-β_friction+(arccos(F_shr/R_o)) or Shear Angle in Machining = Rake Angle in Machining-Friction Angle in Machining+(arccos(Force Along Shear Plane in Machining/Resultant Force in Machining)). Rake angle in machining the angle of orientation of tool’s rake surface from the reference plane and measured on machine longitudinal plane, Friction angle in machining is termed as the angle between the tool and chip, which resists the flow of the chip along the rake face of the tool is friction force, Force along shear plane in machining is the shear force along the shear plane & Resultant force in machining is the vector sum of cutting force and thrust force.

How to calculate Shear angle for given Resultant force, force along shear force, friction, and normal rake angles?

Shear angle for given Resultant force, force along shear force, friction, and normal rake angles is inclination between the shear plane and longitudinal plane is calculated using Shear Angle in Machining = Rake Angle in Machining-Friction Angle in Machining+(arccos(Force Along Shear Plane in Machining/Resultant Force in Machining)). To calculate Shear angle for given Resultant force, force along shear force, friction, and normal rake angles, you need Rake Angle in Machining (α_rake), Friction Angle in Machining (β_friction), Force Along Shear Plane in Machining (F_shr) & Resultant Force in Machining (R_o). With our tool, you need to enter the respective value for Rake Angle in Machining, Friction Angle in Machining, Force Along Shear Plane in Machining & Resultant Force in Machining 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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