Working minor cutting edge Angle given Roughness value Solution

STEP 0: Pre-Calculation Summary
Formula Used
Working Minor Cutting Edge = (acot((Feed/(4*Roughness Value))-cot(Working Major Cutting-Edge Angle)))
Kre' = (acot((f/(4*Ra))-cot(Kre)))
This formula uses 2 Functions, 4 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)
acot - The ACOT function calculates the arccotangent of a given number which is an angle given in radians from 0 (zero) to pi., acot(Number)
Variables Used
Working Minor Cutting Edge - (Measured in Radian) - Working Minor Cutting Edge is the remainder of the cutting edge, where present, commences at the point on the cutting edge where is zero.
Feed - (Measured in Meter) - The Feed is the distance the cutting tool advances along the length of the work for every revolution of the spindle.
Roughness Value - (Measured in Meter) - Roughness Value is the arithmetic average of the absolute values of the roughness profile ordinates.
Working Major Cutting-Edge Angle - (Measured in Radian) - The Working Major Cutting-edge Angle is that entire part of the cutting edge which commences at the point where the working cutting edge is zero.
STEP 1: Convert Input(s) to Base Unit
Feed: 0.9 Millimeter --> 0.0009 Meter (Check conversion here)
Roughness Value: 0.017067 Millimeter --> 1.7067E-05 Meter (Check conversion here)
Working Major Cutting-Edge Angle: 45 Degree --> 0.785398163397301 Radian (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Kre' = (acot((f/(4*Ra))-cot(Kre))) --> (acot((0.0009/(4*1.7067E-05))-cot(0.785398163397301)))
Evaluating ... ...
Kre' = 0.0818957419130501
STEP 3: Convert Result to Output's Unit
0.0818957419130501 Radian -->4.6922803717113 Degree (Check conversion here)
FINAL ANSWER
4.6922803717113 4.69228 Degree <-- Working Minor Cutting Edge
(Calculation completed in 00.004 seconds)

Credits

Created by Parul Keshav
National Institute of Technology (NIT), Srinagar
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National Institute Of Technology (NIT), Hamirpur
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17 Cutting Fluid and Surface Roughness Calculators

Frictional Force required to continuously shear junction between surfaces
Go Force of Friction = Real Area of Contact*((Proportion of Area of Metallic Contact*Shear Strength of Softer Metal)+((1-Proportion of Area of Metallic Contact)*Shear Strength of Softer Lubricant Layer))
Shear Strength of Softer Lubricant layer given Frictional force
Go Shear Strength of Softer Lubricant Layer = ((Force of Friction/Real Area of Contact)-(Proportion of Area of Metallic Contact*Shear Strength of Softer Metal))/(1-Proportion of Area of Metallic Contact)
Area of contact given Frictional Force
Go Real Area of Contact = Force of Friction/((Proportion of Area of Metallic Contact*Shear Strength of Softer Metal)+((1-Proportion of Area of Metallic Contact)*Shear Strength of Softer Lubricant Layer))
Proportion of Area in which metallic contact occurs given Frictional Force
Go Proportion of Area of Metallic Contact = ((Force of Friction/Real Area of Contact)-Shear Strength of Softer Lubricant Layer)/(Shear Strength of Softer Metal-Shear Strength of Softer Lubricant Layer)
Shear Strength of Softer Metal given Frictional force
Go Shear Strength of Softer Metal = ((Force of Friction/Real Area of Contact)-(1-Proportion of Area of Metallic Contact)*Shear Strength of Softer Lubricant Layer)/Proportion of Area of Metallic Contact
Working major cutting edge Angle given Roughness value
Go Working Major Cutting-Edge Angle = (acot((Feed/(4*Roughness Value))-cot(Working Minor Cutting Edge)))
Working minor cutting edge Angle given Roughness value
Go Working Minor Cutting Edge = (acot((Feed/(4*Roughness Value))-cot(Working Major Cutting-Edge Angle)))
Roughness Value
Go Roughness Value = Feed/(4*(cot(Working Major Cutting-Edge Angle)+cot(Working Minor Cutting Edge)))
Feed given Roughness value
Go Feed = 4*(cot(Working Major Cutting-Edge Angle)+cot(Working Minor Cutting Edge))*Roughness Value
Rotational Frequency of Cutter given Roughness Value
Go Rotational Frequency of Cutter = sqrt(0.0642/(Roughness Value*Diameter of Cutter))*Feed Speed
Feed speed given Roughness value
Go Feed Speed = sqrt(Roughness Value*Diameter of Cutter/0.0642)*Rotational Frequency of Cutter
Diameter of Cutter given Roughness Value
Go Diameter of Cutter = (0.0642*(Feed Speed)^2)/(Roughness Value*(Rotational Frequency of Cutter)^2)
Roughness value given feed speed
Go Roughness Value = (0.0642*(Feed Speed)^2)/(Diameter of Cutter*(Rotational Frequency of Cutter)^2)
Feed given Roughness Value and corner radius
Go Feed = (Roughness Value*Corner Radius of Tool/0.0321)^(1/2)
Corner Radius given Roughness value
Go Corner Radius of Tool = 0.0321*(Feed)^2/Roughness Value
Roughness value given corner radius
Go Roughness Value = 0.0321*(Feed)^2/Corner Radius of Tool
Roughness value of tool
Go Roughness Value = 0.0321*(Feed)^2/Corner Radius of Tool

Working minor cutting edge Angle given Roughness value Formula

Working Minor Cutting Edge = (acot((Feed/(4*Roughness Value))-cot(Working Major Cutting-Edge Angle)))
Kre' = (acot((f/(4*Ra))-cot(Kre)))

What is RA and RZ value?

Ra measures the average length between the peaks and valleys and the deviation from the mean line on the entire surface within the sampling length. Rz measures the vertical distance from the highest peak to the lowest valley within five sampling lengths and averages the distances.

How to Calculate Working minor cutting edge Angle given Roughness value?

Working minor cutting edge Angle given Roughness value calculator uses Working Minor Cutting Edge = (acot((Feed/(4*Roughness Value))-cot(Working Major Cutting-Edge Angle))) to calculate the Working Minor Cutting Edge, The Working minor cutting edge Angle given Roughness value formula is used to find the remainder of the cutting edge, where present, commences at the point on the cutting edge where the working cutting edge angle is zero. Working Minor Cutting Edge is denoted by Kre' symbol.

How to calculate Working minor cutting edge Angle given Roughness value using this online calculator? To use this online calculator for Working minor cutting edge Angle given Roughness value, enter Feed (f), Roughness Value (Ra) & Working Major Cutting-Edge Angle (Kre) and hit the calculate button. Here is how the Working minor cutting edge Angle given Roughness value calculation can be explained with given input values -> 268.8479 = (acot((0.0009/(4*1.7067E-05))-cot(0.785398163397301))).

FAQ

What is Working minor cutting edge Angle given Roughness value?
The Working minor cutting edge Angle given Roughness value formula is used to find the remainder of the cutting edge, where present, commences at the point on the cutting edge where the working cutting edge angle is zero and is represented as Kre' = (acot((f/(4*Ra))-cot(Kre))) or Working Minor Cutting Edge = (acot((Feed/(4*Roughness Value))-cot(Working Major Cutting-Edge Angle))). The Feed is the distance the cutting tool advances along the length of the work for every revolution of the spindle, Roughness Value is the arithmetic average of the absolute values of the roughness profile ordinates & The Working Major Cutting-edge Angle is that entire part of the cutting edge which commences at the point where the working cutting edge is zero.
How to calculate Working minor cutting edge Angle given Roughness value?
The Working minor cutting edge Angle given Roughness value formula is used to find the remainder of the cutting edge, where present, commences at the point on the cutting edge where the working cutting edge angle is zero is calculated using Working Minor Cutting Edge = (acot((Feed/(4*Roughness Value))-cot(Working Major Cutting-Edge Angle))). To calculate Working minor cutting edge Angle given Roughness value, you need Feed (f), Roughness Value (Ra) & Working Major Cutting-Edge Angle (Kre). With our tool, you need to enter the respective value for Feed, Roughness Value & Working Major Cutting-Edge Angle 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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