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

GoR in merchant circle for given force along shear force, shear, 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' c \cdot \sec (β' - α')

R^' - Resultant Force on Workpiece?F'_c - Cutting Force on Workpiece?β^' - Machining Friction Angle?α^' - Cutting Tool Rake Angle?

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

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

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

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

170.0016 = 150 \cdot \sec (36.695 - 8.6215)

170.0016N = 150N \cdot \sec (36.695° - 8.6215°)

170.0016 = 150 \cdot \sec (36.695 - 8.6215)

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

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

FIRST Step Consider the formula

R' = F' c \cdot \sec (β' - α')

Next Step Substitute values of Variables

∴

R' = 150N \cdot \sec (36.695° - 8.6215°)

Next Step Convert Units

∴

R' = 150N \cdot \sec (0.6404rad - 0.1505rad)

Next Step Prepare to Evaluate

∴

R' = 150 \cdot \sec (0.6404 - 0.1505)

Next Step Evaluate

∴

R' = 170.001603146661N

LAST Step Rounding Answer

∴

R' = 170.0016N

Resultant force in merchant circle for given cutting force, 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

Cutting Force on Workpiece

Cutting force on workpiece is the force in the direction of cutting, the same direction as the cutting speed.

Symbol: F'_c

Measurement: ForceUnit: N

Note: Value should be greater than 0.

Formulas to find Cutting Force on Workpiece

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

R' = F s \cdot \sec (ϕ' + 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 Resultant force in merchant circle for given cutting force, friction and normal rake angles?

Resultant force in merchant circle for given cutting force, friction and normal rake angles evaluator uses Resultant Force on Workpiece = Cutting Force on Workpiece*sec(Machining Friction Angle-Cutting Tool Rake Angle) to evaluate the Resultant Force on Workpiece, Resultant force in merchant circle for given cutting force, friction and normal rake angles is defined as the resultant of cutting and thrust forces. Resultant Force on Workpiece is denoted by R^' symbol.

How to evaluate Resultant force in merchant circle for given cutting force, friction and normal rake angles using this online evaluator? To use this online evaluator for Resultant force in merchant circle for given cutting force, friction and normal rake angles, enter Cutting Force on Workpiece (F'_c), Machining Friction Angle (β^') & Cutting Tool Rake Angle (α^') and hit the calculate button.

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

What is the formula to find Resultant force in merchant circle for given cutting force, friction and normal rake angles?

The formula of Resultant force in merchant circle for given cutting force, friction and normal rake angles is expressed as Resultant Force on Workpiece = Cutting Force on Workpiece*sec(Machining Friction Angle-Cutting Tool Rake Angle). Here is an example- 170.0016 = 150*sec(0.640448569019199-0.150473561460663).

How to calculate Resultant force in merchant circle for given cutting force, friction and normal rake angles?

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

Can the Resultant force in merchant circle for given cutting force, friction and normal rake angles be negative?

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

Which unit is used to measure Resultant force in merchant circle for given cutting force, friction and normal rake angles?

Resultant force in merchant circle for given cutting force, 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 Resultant force in merchant circle for given cutting force, friction and normal rake angles can be measured.

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