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

✖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%
✖Force produced along shear plane Force Produced Along Shear Plane.ⓘ Force Produced Along Shear Plane [F_s]			+10% -10%
✖Resultant force on workpiece is the vector sum of cutting force and thrust force.ⓘ Resultant Force on Workpiece [R^']			+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.ⓘ Normal rake angle for given Resultant force, force along shear, shear, and friction angle [α^']

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

Formula

`"α"^{"'"} = "ϕ"^{"'"}+"β"^{"'"}-(arccos("F"_{"s"}/"R"^{"'"}))`

Example

`"8.621522°"="27.3°"+"36.695°"-(arccos("96.5982N"/"170N"))`

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

STEP 0: Pre-Calculation Summary

Formula Used

Cutting Tool Rake Angle = Shear Angle for Metal Cutting+Machining Friction Angle-(arccos(Force Produced Along Shear Plane/Resultant Force on Workpiece))
α^' = ϕ^'+β^'-(arccos(F_s/R^'))
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

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.
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.
Force Produced Along Shear Plane - (Measured in Newton) - Force produced along shear plane Force Produced Along Shear Plane.
Resultant Force on Workpiece - (Measured in Newton) - Resultant force on workpiece is the vector sum of cutting force and thrust force.

STEP 1: Convert Input(s) to Base Unit

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)
Force Produced Along Shear Plane: 96.5982 Newton --> 96.5982 Newton No Conversion Required
Resultant Force on Workpiece: 170 Newton --> 170 Newton No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

α^' = ϕ^'+β^'-(arccos(F_s/R^')) --> 0.476474885794362+0.640448569019199-(arccos(96.5982/170))

Evaluating ... ...

α^' = 0.150473939311218

STEP 3: Convert Result to Output's Unit

0.150473939311218 Radian -->8.6215216492421 Degree (Check conversion here)

FINAL ANSWER

8.6215216492421 ≈ 8.621522 Degree <-- Cutting Tool Rake Angle

(Calculation completed in 00.004 seconds)

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Home » Engineering » Production Engineering » Metal Cutting » Merchant Force Circle » Resultants and Stress » Normal rake angle for given Resultant force, force along shear, shear, and friction angle

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!

< 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

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

Cutting Tool Rake Angle = Shear Angle for Metal Cutting+Machining Friction Angle-(arccos(Force Produced Along Shear Plane/Resultant Force on Workpiece))
α^' = ϕ^'+β^'-(arccos(F_s/R^'))

What is Normal rake angle

Normal rake angle is a parameter used in various cutting and machining processes, describing the angle of the cutting face relative to the work. It is defined is the angle of orientation of the tool's rake surface from the reference plane and measured on a normal plane

How to Calculate Normal rake angle for given Resultant force, force along shear, shear, and friction angle?

Normal rake angle for given Resultant force, force along shear, shear, and friction angle calculator uses Cutting Tool Rake Angle = Shear Angle for Metal Cutting+Machining Friction Angle-(arccos(Force Produced Along Shear Plane/Resultant Force on Workpiece)) to calculate the Cutting Tool Rake Angle, Normal rake angle for given Resultant force, force along shear, shear, and friction angles is defined as the angle of orientation of the tool's rake surface from the reference plane and measured on a normal plane. Cutting Tool Rake Angle is denoted by α^' symbol.

How to calculate Normal rake angle for given Resultant force, force along shear, shear, and friction angle using this online calculator? To use this online calculator for Normal rake angle for given Resultant force, force along shear, shear, and friction angle, enter Shear Angle for Metal Cutting (ϕ^'), Machining Friction Angle (β^'), Force Produced Along Shear Plane (F_s) & Resultant Force on Workpiece (R^') and hit the calculate button. Here is how the Normal rake angle for given Resultant force, force along shear, shear, and friction angle calculation can be explained with given input values -> 494.019 = 0.476474885794362+0.640448569019199-(arccos(96.5982/170)).

FAQ

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

Normal rake angle for given Resultant force, force along shear, shear, and friction angles is defined as the angle of orientation of the tool's rake surface from the reference plane and measured on a normal plane and is represented as α^' = ϕ^'+β^'-(arccos(F_s/R^')) or Cutting Tool Rake Angle = Shear Angle for Metal Cutting+Machining Friction Angle-(arccos(Force Produced Along Shear Plane/Resultant Force on Workpiece)). 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, Force produced along shear plane Force Produced Along Shear Plane & Resultant force on workpiece is the vector sum of cutting force and thrust force.

How to calculate Normal rake angle for given Resultant force, force along shear, shear, and friction angle?

Normal rake angle for given Resultant force, force along shear, shear, and friction angles is defined as the angle of orientation of the tool's rake surface from the reference plane and measured on a normal plane is calculated using Cutting Tool Rake Angle = Shear Angle for Metal Cutting+Machining Friction Angle-(arccos(Force Produced Along Shear Plane/Resultant Force on Workpiece)). To calculate Normal rake angle for given Resultant force, force along shear, shear, and friction angle, you need Shear Angle for Metal Cutting (ϕ^'), Machining Friction Angle (β^'), Force Produced Along Shear Plane (F_s) & Resultant Force on Workpiece (R^'). With our tool, you need to enter the respective value for Shear Angle for Metal Cutting, Machining Friction Angle, Force Produced Along Shear Plane & Resultant Force on Workpiece 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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