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

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

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Resultant force on workpiece is the vector sum of cutting force and thrust force. Check FAQs

R' = F s \cdot \sec (ϕ' + β' - α')

R^' - Resultant Force on Workpiece?F_s - Force Produced Along Shear Plane?ϕ^' - Shear Angle for Metal Cutting?β^' - Machining Friction Angle?α^' - Cutting Tool Rake Angle?

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

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Here is how the R in merchant circle for given force along shear force, shear, friction and normal rake angles equation looks like with Values.

Here is how the R in merchant circle for given force along shear force, shear, friction and normal rake angles equation looks like with Units.

Here is how the R in merchant circle for given force along shear force, shear, friction and normal rake angles equation looks like.

170.0001 = 96.5982 \cdot \sec (27.3 + 36.695 - 8.6215)

170.0001N = 96.5982N \cdot \sec (27.3° + 36.695° - 8.6215°)

170.0001 = 96.5982 \cdot \sec (27.3 + 36.695 - 8.6215)

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

Follow our step by step solution on how to calculate R in merchant circle for given force along shear force, shear, friction and normal rake angles?

FIRST Step Consider the formula

R' = F s \cdot \sec (ϕ' + β' - α')

Next Step Substitute values of Variables

∴

R' = 96.5982N \cdot \sec (27.3° + 36.695° - 8.6215°)

Next Step Convert Units

∴

R' = 96.5982N \cdot \sec (0.4765rad + 0.6404rad - 0.1505rad)

Next Step Prepare to Evaluate

∴

R' = 96.5982 \cdot \sec (0.4765 + 0.6404 - 0.1505)

Next Step Evaluate

∴

R' = 170.000093021258N

LAST Step Rounding Answer

∴

R' = 170.0001N

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

Variables

Functions

Resultant Force on Workpiece

Resultant force on workpiece is the vector sum of cutting force and thrust force.

Symbol: R^'

Measurement: ForceUnit: N

Note: Value can be positive or negative.

Formulas to find Resultant Force on Workpiece

Force Produced Along Shear Plane

The force produced along shear plane is the internal force that causes material layers to slide past each other when subjected to shear stress.

Symbol: F_s

Measurement: ForceUnit: N

Note: Value can be positive or negative.

Formulas to find Force Produced Along Shear Plane

Shear Angle for Metal Cutting

Shear angle for metal cutting is the inclination of the shear plane with the horizontal axis at machining point.

Symbol: ϕ^'

Measurement: AngleUnit: °

Note: Value should be greater than 0.

Formulas to find Shear Angle for Metal Cutting

Machining Friction Angle

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.

Symbol: β^'

Measurement: AngleUnit: °

Note: Value should be greater than 0.

Formulas to find Machining Friction Angle

Cutting Tool Rake Angle

Cutting tool rake angle is the angle of orientation of tool’s rake surface from the reference plane and measured on machine longitudinal plane.

Symbol: α^'

Measurement: AngleUnit: °

Note: Value can be positive or negative.

Formulas to find Cutting Tool Rake Angle

sec

Secant is a trigonometric function that is defined ratio of the hypotenuse to the shorter side adjacent to an acute angle (in a right-angled triangle); the reciprocal of a cosine.

Syntax: sec(Angle)

Other Formulas to find Resultant Force on Workpiece

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

R' = F' c \cdot \sec (β' - α')

Other formulas in Resultants and Stress category

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

F N = F' c \cdot \cos (α' N) - F' t \cdot \sin (α' N)

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

σ n = \frac{F N}{A shear}

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

α' = ϕ' + β' - \arccos (\frac{F s}{R'})

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

τ s = F' c \cdot \frac{\cos (ϕ' + β' - α')}{w cut \cdot t 1 \cdot \cos (β' - α')}

How to Evaluate R in merchant circle for given force along shear force, shear, friction and normal rake angles?

R in merchant circle for given force along shear force, shear, friction and normal rake angles evaluator uses Resultant Force on Workpiece = Force Produced Along Shear Plane*sec(Shear Angle for Metal Cutting+Machining Friction Angle-Cutting Tool Rake Angle) to evaluate the Resultant Force on Workpiece, R in merchant circle for given force along shear force, shear, friction and normal rake angles is the resultant of shear force and normal force on shear plane. Resultant Force on Workpiece is denoted by R^' symbol.

How to evaluate R in merchant circle for given force along shear force, shear, friction and normal rake angles using this online evaluator? To use this online evaluator for R in merchant circle for given force along shear force, shear, friction and normal rake angles, enter Force Produced Along Shear Plane (F_s), Shear Angle for Metal Cutting (ϕ^'), Machining Friction Angle (β^') & Cutting Tool Rake Angle (α^') and hit the calculate button.

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

What is the formula to find R in merchant circle for given force along shear force, shear, friction and normal rake angles?

The formula of R in merchant circle for given force along shear force, shear, friction and normal rake angles is expressed as Resultant Force on Workpiece = Force Produced Along Shear Plane*sec(Shear Angle for Metal Cutting+Machining Friction Angle-Cutting Tool Rake Angle). Here is an example- 170.0001 = 96.5982*sec(0.476474885794362+0.640448569019199-0.150473561460663).

How to calculate R in merchant circle for given force along shear force, shear, friction and normal rake angles?

With Force Produced Along Shear Plane (F_s), Shear Angle for Metal Cutting (ϕ^'), Machining Friction Angle (β^') & Cutting Tool Rake Angle (α^') we can find R in merchant circle for given force along shear force, shear, friction and normal rake angles using the formula - Resultant Force on Workpiece = Force Produced Along Shear Plane*sec(Shear Angle for Metal Cutting+Machining Friction Angle-Cutting Tool Rake Angle). This formula also uses Secant (sec) function(s).

What are the other ways to Calculate Resultant Force on Workpiece?

Here are the different ways to Calculate Resultant Force on Workpiece-

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

Can the R in merchant circle for given force along shear force, shear, friction and normal rake angles be negative?

Yes, the R in merchant circle for given force along shear force, shear, friction and normal rake angles, measured in Force can be negative.

Which unit is used to measure R in merchant circle for given force along shear force, shear, friction and normal rake angles?

R in merchant circle for given force along shear force, shear, friction and normal rake angles is usually measured using the Newton[N] for Force. Exanewton[N], Meganewton[N], Kilonewton[N] are the few other units in which R in merchant circle for given force along shear force, shear, friction and normal rake angles can be measured.

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

​GoResultant force in merchant circle for given cutting force, friction and normal rake angles Formula

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

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

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

Other Formulas to find Resultant Force on Workpiece

Other formulas in Resultants and Stress category

How to Evaluate R in merchant circle for given force along shear force, shear, friction and normal rake angles?

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

Variable Name

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