Cutting Ratio for given Shear Angle of Continuous chip Solution

STEP 0: Pre-Calculation Summary
Formula Used
Cutting Ratio = tan(Shear angle)/(cos(Working Normal Rake)+(tan(Shear angle)*sin(Working Normal Rake)))
rc = tan(ϕ)/(cos(γne)+(tan(ϕ)*sin(γne)))
This formula uses 3 Functions, 3 Variables
Functions Used
sin - Sine is a trigonometric function that describes the ratio of the length of the opposite side of a right triangle to the length of the hypotenuse., sin(Angle)
cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., cos(Angle)
tan - The tangent of an angle is a trigonometric ratio of the length of the side opposite an angle to the length of the side adjacent to an angle in a right triangle., tan(Angle)
Variables Used
Cutting Ratio - The Cutting Ratio is defined as the thickness of metal before cutting to the thickness of metal after cutting.
Shear angle - (Measured in Radian) - Shear angle is the inclination of the shear plane with the horizontal axis at machining point.
Working Normal Rake - (Measured in Radian) - The Working Normal Rake angle is the angle of orientation of the tool's rake surface from the reference plane and measured on a normal plane.
STEP 1: Convert Input(s) to Base Unit
Shear angle: 11.406 Degree --> 0.199072254482436 Radian (Check conversion here)
Working Normal Rake: 20 Degree --> 0.3490658503988 Radian (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
rc = tan(ϕ)/(cos(γne)+(tan(ϕ)*sin(γne))) --> tan(0.199072254482436)/(cos(0.3490658503988)+(tan(0.199072254482436)*sin(0.3490658503988)))
Evaluating ... ...
rc = 0.200005649498844
STEP 3: Convert Result to Output's Unit
0.200005649498844 --> No Conversion Required
FINAL ANSWER
0.200005649498844 0.200006 <-- Cutting Ratio
(Calculation completed in 00.004 seconds)

Credits

Created by Parul Keshav
National Institute of Technology (NIT), Srinagar
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13 Mechanics of Metal Cutting Calculators

Cutting Ratio for given Shear Angle of Continuous chip
Go Cutting Ratio = tan(Shear angle)/(cos(Working Normal Rake)+(tan(Shear angle)*sin(Working Normal Rake)))
Shear Angle of Continuous Chip Formation
Go Shear angle = atan((Cutting Ratio*cos(Working Normal Rake))/(1-(Cutting Ratio*sin(Working Normal Rake))))
Total Shear force by tool
Go Total Shear Force by Tool = (Cutting Force*cos(Shear angle))+(Thrust force*sin(Shear angle))
Density of Workpiece given Thickness of Chip
Go Density of work piece = Mass of Chip/(Chip Thickness*Length of Chip*Width of Chip)
Rate of Energy Consumption during Machining given Specific Cutting Energy
Go Rate of Energy Consumption during Machining = Specific Cutting Energy in Machining*Metal removal rate
Metal Removal Rate given Specific Cutting Energy
Go Metal removal rate = Rate of Energy Consumption during Machining/Specific Cutting Energy in Machining
Specific cutting energy in machining
Go Specific Cutting Energy in Machining = Rate of Energy Consumption during Machining/Metal removal rate
Area of Shear
Go Area of Shear = Cross-sectional Area of Uncut Chip/sin(Shear angle)
Cutting Speed using Rate of Energy Consumption during Machining
Go Cutting Speed = Rate of Energy Consumption during Machining/Cutting Force
Rate of Energy Consumption during Machining
Go Rate of Energy Consumption during Machining = Cutting Speed*Cutting Force
Plowing Force using Force required to remove Chip
Go Plowing Force = Resultant Cutting Force-Force Required to Remove Chip
Shear Strength of Material on Shear Plane
Go Shear Strength of Material = Total Shear Force by Tool/Area of Shear
Cutting Ratio
Go Cutting Ratio = Undeformed Chip Thickness/Uncut Chip Thickness

Cutting Ratio for given Shear Angle of Continuous chip Formula

Cutting Ratio = tan(Shear angle)/(cos(Working Normal Rake)+(tan(Shear angle)*sin(Working Normal Rake)))
rc = tan(ϕ)/(cos(γne)+(tan(ϕ)*sin(γne)))

What is Uncut Chip Thickness?

Uncut chip thickness is comparable to cutting edge radius in micromachining. If the uncut chip thickness is less than a critical value, there will be no chip formation. This critical value is termed as minimum uncut chip thickness.

How to Calculate Cutting Ratio for given Shear Angle of Continuous chip?

Cutting Ratio for given Shear Angle of Continuous chip calculator uses Cutting Ratio = tan(Shear angle)/(cos(Working Normal Rake)+(tan(Shear angle)*sin(Working Normal Rake))) to calculate the Cutting Ratio, The Cutting Ratio for given Shear Angle of Continuous chip is defined as the thickness of metal before cutting to the thickness of metal after cutting. Cutting Ratio is denoted by rc symbol.

How to calculate Cutting Ratio for given Shear Angle of Continuous chip using this online calculator? To use this online calculator for Cutting Ratio for given Shear Angle of Continuous chip, enter Shear angle (ϕ) & Working Normal Rake ne) and hit the calculate button. Here is how the Cutting Ratio for given Shear Angle of Continuous chip calculation can be explained with given input values -> 0.200006 = tan(0.199072254482436)/(cos(0.3490658503988)+(tan(0.199072254482436)*sin(0.3490658503988))).

FAQ

What is Cutting Ratio for given Shear Angle of Continuous chip?
The Cutting Ratio for given Shear Angle of Continuous chip is defined as the thickness of metal before cutting to the thickness of metal after cutting and is represented as rc = tan(ϕ)/(cos(γne)+(tan(ϕ)*sin(γne))) or Cutting Ratio = tan(Shear angle)/(cos(Working Normal Rake)+(tan(Shear angle)*sin(Working Normal Rake))). Shear angle is the inclination of the shear plane with the horizontal axis at machining point & The Working Normal Rake angle is the angle of orientation of the tool's rake surface from the reference plane and measured on a normal plane.
How to calculate Cutting Ratio for given Shear Angle of Continuous chip?
The Cutting Ratio for given Shear Angle of Continuous chip is defined as the thickness of metal before cutting to the thickness of metal after cutting is calculated using Cutting Ratio = tan(Shear angle)/(cos(Working Normal Rake)+(tan(Shear angle)*sin(Working Normal Rake))). To calculate Cutting Ratio for given Shear Angle of Continuous chip, you need Shear angle (ϕ) & Working Normal Rake ne). With our tool, you need to enter the respective value for Shear angle & Working Normal Rake and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
How many ways are there to calculate Cutting Ratio?
In this formula, Cutting Ratio uses Shear angle & Working Normal Rake. We can use 1 other way(s) to calculate the same, which is/are as follows -
  • Cutting Ratio = Undeformed Chip Thickness/Uncut Chip Thickness
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