Radius of Chip given Chip breaker wedge angle Solution

STEP 0: Pre-Calculation Summary
Formula Used
Radius of Chip Curvature = ((Chip-Breaker Distance-Length of Chip Tool Contact)-(Chip Breaker Height*cot(Chip Breaker Wedge Angle)))*cot(Chip Breaker Wedge Angle/(2))
rchip = ((ln-lf)-(h*cot(σ)))*cot(σ/(2))
This formula uses 1 Functions, 5 Variables
Functions Used
cot - Cotangent is a trigonometric function that is defined as the ratio of the adjacent side to the opposite side in a right triangle., cot(Angle)
Variables Used
Radius of Chip Curvature - (Measured in Meter) - The Radius of Chip Curvature is the constant radius of curvature maintained by the chip until it breaks away or clears the chip breaker.
Chip-Breaker Distance - (Measured in Meter) - Chip-Breaker Distance is defined as the distance between the tool point and the chip breaker.
Length of Chip Tool Contact - (Measured in Meter) - The Length of Chip Tool Contact is the distance over which a continuous chip flows over the tool rake face while maintaining contact.
Chip Breaker Height - (Measured in Meter) - Chip breaker height is defined as the height of the chip breaker on the tool.
Chip Breaker Wedge Angle - (Measured in Radian) - Chip Breaker Wedge Angle is the angle between the face and flank surface of a single-point cutting tool.
STEP 1: Convert Input(s) to Base Unit
Chip-Breaker Distance: 3.43 Millimeter --> 0.00343 Meter (Check conversion here)
Length of Chip Tool Contact: 1.16 Millimeter --> 0.00116 Meter (Check conversion here)
Chip Breaker Height: 0.8 Millimeter --> 0.0008 Meter (Check conversion here)
Chip Breaker Wedge Angle: 0.81 Radian --> 0.81 Radian No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
rchip = ((ln-lf)-(h*cot(σ)))*cot(σ/(2)) --> ((0.00343-0.00116)-(0.0008*cot(0.81)))*cot(0.81/(2))
Evaluating ... ...
rchip = 0.00351860748995525
STEP 3: Convert Result to Output's Unit
0.00351860748995525 Meter -->3.51860748995525 Millimeter (Check conversion here)
FINAL ANSWER
3.51860748995525 3.518607 Millimeter <-- Radius of Chip Curvature
(Calculation completed in 00.004 seconds)

Credits

Created by Parul Keshav
National Institute of Technology (NIT), Srinagar
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Verified by Kumar Siddhant
Indian Institute of Information Technology, Design and Manufacturing (IIITDM), Jabalpur
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14 Chip Control Calculators

Chip breaker height given Chip breaker wedge angle
Go Chip Breaker Height = ((Chip-Breaker Distance-Length of Chip Tool Contact)-(Radius of Chip Curvature/cot(Chip Breaker Wedge Angle/(2))))/cot(Chip Breaker Wedge Angle)
Radius of Chip given Chip breaker wedge angle
Go Radius of Chip Curvature = ((Chip-Breaker Distance-Length of Chip Tool Contact)-(Chip Breaker Height*cot(Chip Breaker Wedge Angle)))*cot(Chip Breaker Wedge Angle/(2))
Length of chip tool contact given Chip breaker wedge angle
Go Length of Chip Tool Contact = Chip-Breaker Distance-(Radius of Chip Curvature/cot(Chip Breaker Wedge Angle/(2)))-(Chip Breaker Height*cot(Chip Breaker Wedge Angle))
Chip breaker distance given Chip breaker wedge angle
Go Chip-Breaker Distance = Radius of Chip Curvature/cot(Chip Breaker Wedge Angle/(2))+(Chip Breaker Height*cot(Chip Breaker Wedge Angle))+Length of Chip Tool Contact
Radius of chip curvature given constant of material
Go Radius of Chip Curvature = (((Chip-Breaker Distance)-((Material Constant)*(Chip Thickness))^2)/(2*(Chip Breaker Height)))+(Chip Breaker Height/2)
Length of chip tool contact given radius of chip curvature
Go Length of Chip Tool Contact = Chip-Breaker Distance-sqrt((Radius of Chip Curvature*2*Chip Breaker Height)-(Chip Breaker Height^2))
Chip breaker distance given radius of chip curvature
Go Chip-Breaker Distance = sqrt((Radius of Chip Curvature*2*Chip Breaker Height)-(Chip Breaker Height^2))+Length of Chip Tool Contact
Chip break distance when material constant is unity
Go Chip-Breaker Distance = sqrt((Radius of Chip Curvature*2*Chip Breaker Height)-(Chip Breaker Height^2))+Chip Thickness
Chip Thickness when material constant is unity
Go Chip Thickness = Chip-Breaker Distance-sqrt((Radius of Chip Curvature*2*Chip Breaker Height)-(Chip Breaker Height^2))
Radius of Chip curvature
Go Radius of Chip Curvature = ((Chip-Breaker Distance-Length of Chip Tool Contact)^2)/(2*Chip Breaker Height)+(Chip Breaker Height/2)
Radius of Chip curvature when material constant is unity
Go Radius of Chip Curvature = ((Chip-Breaker Distance-Chip Thickness)^2)/(2*Chip Breaker Height)+(Chip Breaker Height/2)
Chip thickness given length of chip tool contact
Go Chip Thickness = Length of Chip Tool Contact/Material Constant
Constant for length of chip tool contact
Go Material Constant = Length of Chip Tool Contact/Chip Thickness
Length of chip tool contact
Go Length of Chip Tool Contact = Chip Thickness*Material Constant

Radius of Chip given Chip breaker wedge angle Formula

Radius of Chip Curvature = ((Chip-Breaker Distance-Length of Chip Tool Contact)-(Chip Breaker Height*cot(Chip Breaker Wedge Angle)))*cot(Chip Breaker Wedge Angle/(2))
rchip = ((ln-lf)-(h*cot(σ)))*cot(σ/(2))

Which angle is control the geometry of chip formation?

Clearance angles and rake angles are important to chip formation and control. Clearance angles are used to decrease the amount of rubbing of the tool against the workpiece and are always positive or zero, never negative.

How to Calculate Radius of Chip given Chip breaker wedge angle?

Radius of Chip given Chip breaker wedge angle calculator uses Radius of Chip Curvature = ((Chip-Breaker Distance-Length of Chip Tool Contact)-(Chip Breaker Height*cot(Chip Breaker Wedge Angle)))*cot(Chip Breaker Wedge Angle/(2)) to calculate the Radius of Chip Curvature, The Radius of Chip given Chip breaker wedge angle is the radius that maintains a constant radius of curvature until it breaks away or clears the chip breaker. Radius of Chip Curvature is denoted by rchip symbol.

How to calculate Radius of Chip given Chip breaker wedge angle using this online calculator? To use this online calculator for Radius of Chip given Chip breaker wedge angle, enter Chip-Breaker Distance (ln), Length of Chip Tool Contact (lf), Chip Breaker Height (h) & Chip Breaker Wedge Angle (σ) and hit the calculate button. Here is how the Radius of Chip given Chip breaker wedge angle calculation can be explained with given input values -> -4464.839672 = ((0.00343-0.00116)-(0.0008*cot(0.81)))*cot(0.81/(2)).

FAQ

What is Radius of Chip given Chip breaker wedge angle?
The Radius of Chip given Chip breaker wedge angle is the radius that maintains a constant radius of curvature until it breaks away or clears the chip breaker and is represented as rchip = ((ln-lf)-(h*cot(σ)))*cot(σ/(2)) or Radius of Chip Curvature = ((Chip-Breaker Distance-Length of Chip Tool Contact)-(Chip Breaker Height*cot(Chip Breaker Wedge Angle)))*cot(Chip Breaker Wedge Angle/(2)). Chip-Breaker Distance is defined as the distance between the tool point and the chip breaker, The Length of Chip Tool Contact is the distance over which a continuous chip flows over the tool rake face while maintaining contact, Chip breaker height is defined as the height of the chip breaker on the tool & Chip Breaker Wedge Angle is the angle between the face and flank surface of a single-point cutting tool.
How to calculate Radius of Chip given Chip breaker wedge angle?
The Radius of Chip given Chip breaker wedge angle is the radius that maintains a constant radius of curvature until it breaks away or clears the chip breaker is calculated using Radius of Chip Curvature = ((Chip-Breaker Distance-Length of Chip Tool Contact)-(Chip Breaker Height*cot(Chip Breaker Wedge Angle)))*cot(Chip Breaker Wedge Angle/(2)). To calculate Radius of Chip given Chip breaker wedge angle, you need Chip-Breaker Distance (ln), Length of Chip Tool Contact (lf), Chip Breaker Height (h) & Chip Breaker Wedge Angle (σ). With our tool, you need to enter the respective value for Chip-Breaker Distance, Length of Chip Tool Contact, Chip Breaker Height & Chip Breaker Wedge Angle 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 Radius of Chip Curvature?
In this formula, Radius of Chip Curvature uses Chip-Breaker Distance, Length of Chip Tool Contact, Chip Breaker Height & Chip Breaker Wedge Angle. We can use 3 other way(s) to calculate the same, which is/are as follows -
  • Radius of Chip Curvature = (((Chip-Breaker Distance)-((Material Constant)*(Chip Thickness))^2)/(2*(Chip Breaker Height)))+(Chip Breaker Height/2)
  • Radius of Chip Curvature = ((Chip-Breaker Distance-Length of Chip Tool Contact)^2)/(2*Chip Breaker Height)+(Chip Breaker Height/2)
  • Radius of Chip Curvature = ((Chip-Breaker Distance-Chip Thickness)^2)/(2*Chip Breaker Height)+(Chip Breaker Height/2)
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