Instantaneous Radius for Cut given Rate of Increase of Wear-Land Solution

STEP 0: Pre-Calculation Summary
Formula Used
Instantaneous Radius for Cut = (Reference Cutting Velocity*((Rate of Increase of Wear Land Width*Reference Tool Life/Maximum Wear Land Width)^Taylor's Tool Life Exponent))/(2*pi*Rotational Frequency of Spindle)
r = (Vref*((dVBdtratio*Tref/VBm)^n))/(2*pi*ns)
This formula uses 1 Constants, 7 Variables
Constants Used
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
Variables Used
Instantaneous Radius for Cut - (Measured in Meter) - Instantaneous Radius for Cut is the radius of the workpiece surface currently being machined.
Reference Cutting Velocity - (Measured in Meter per Second) - Reference Cutting Velocity is the Cutting Velocity of the tool used in the reference Machining Condition.
Rate of Increase of Wear Land Width - (Measured in Meter per Second) - Rate of Increase of Wear Land Width is the increase in the width of the region where wear occurs in a tool per unit time.
Reference Tool Life - (Measured in Second) - Reference Tool Life is the Tool Life of the tool obtained in the reference Machining Condition.
Maximum Wear Land Width - (Measured in Meter) - Maximum Wear Land Width is the maximum width of the region where wear occurs in a tool.
Taylor's Tool Life Exponent - Taylor's Tool Life Exponent is an experimental exponent that helps in quantifying the rate of Tool Wear.
Rotational Frequency of Spindle - (Measured in Hertz) - Rotational Frequency of Spindle is the number of turns made by the spindle of the Machine for cutting in one second.
STEP 1: Convert Input(s) to Base Unit
Reference Cutting Velocity: 5000 Millimeter per Minute --> 0.0833333333333333 Meter per Second (Check conversion here)
Rate of Increase of Wear Land Width: 0.16 Millimeter per Minute --> 2.66666666666667E-06 Meter per Second (Check conversion here)
Reference Tool Life: 5 Minute --> 300 Second (Check conversion here)
Maximum Wear Land Width: 0.32 Millimeter --> 0.00032 Meter (Check conversion here)
Taylor's Tool Life Exponent: 0.5 --> No Conversion Required
Rotational Frequency of Spindle: 10 Hertz --> 10 Hertz No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
r = (Vref*((dVBdtratio*Tref/VBm)^n))/(2*pi*ns) --> (0.0833333333333333*((2.66666666666667E-06*300/0.00032)^0.5))/(2*pi*10)
Evaluating ... ...
r = 0.00209705050435363
STEP 3: Convert Result to Output's Unit
0.00209705050435363 Meter -->2.09705050435363 Millimeter (Check conversion here)
FINAL ANSWER
2.09705050435363 2.097051 Millimeter <-- Instantaneous Radius for Cut
(Calculation completed in 00.020 seconds)

Credits

Created by Kumar Siddhant
Indian Institute of Information Technology, Design and Manufacturing (IIITDM), Jabalpur
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3 Instantaneous Radius Calculators

Instantaneous Radius for Cut given Rate of Increase of Wear-Land
Go Instantaneous Radius for Cut = (Reference Cutting Velocity*((Rate of Increase of Wear Land Width*Reference Tool Life/Maximum Wear Land Width)^Taylor's Tool Life Exponent))/(2*pi*Rotational Frequency of Spindle)
Instantaneous Radius for Cut
Go Instantaneous Radius for Cut = Outside Radius of the Workpiece-Rotational Frequency of Spindle*Feed*Process Time
Instantaneous Radius for Cut given Cutting Speed
Go Instantaneous Radius for Cut = Cutting Velocity/(2*pi*Rotational Frequency of Spindle)

Instantaneous Radius for Cut given Rate of Increase of Wear-Land Formula

Instantaneous Radius for Cut = (Reference Cutting Velocity*((Rate of Increase of Wear Land Width*Reference Tool Life/Maximum Wear Land Width)^Taylor's Tool Life Exponent))/(2*pi*Rotational Frequency of Spindle)
r = (Vref*((dVBdtratio*Tref/VBm)^n))/(2*pi*ns)

Ideal Capacity of a Machine Tool

The desired characteristics of a Machine Toole are:
1. Powerful and high Strength
2. Rigid and Stable
3. Tools allows much higher Cutting Velocity, if required and permissible
4. Low wear

How to Calculate Instantaneous Radius for Cut given Rate of Increase of Wear-Land?

Instantaneous Radius for Cut given Rate of Increase of Wear-Land calculator uses Instantaneous Radius for Cut = (Reference Cutting Velocity*((Rate of Increase of Wear Land Width*Reference Tool Life/Maximum Wear Land Width)^Taylor's Tool Life Exponent))/(2*pi*Rotational Frequency of Spindle) to calculate the Instantaneous Radius for Cut, The Instantaneous Radius for Cut given Rate of Increase of Wear-Land is a method to determine the maximum radius of the workpiece that can be machined on a given spindle speed when Rate of Increase of Wear-Land is given. Instantaneous Radius for Cut is denoted by r symbol.

How to calculate Instantaneous Radius for Cut given Rate of Increase of Wear-Land using this online calculator? To use this online calculator for Instantaneous Radius for Cut given Rate of Increase of Wear-Land, enter Reference Cutting Velocity (Vref), Rate of Increase of Wear Land Width (dVBdtratio), Reference Tool Life (Tref), Maximum Wear Land Width (VBm), Taylor's Tool Life Exponent (n) & Rotational Frequency of Spindle (ns) and hit the calculate button. Here is how the Instantaneous Radius for Cut given Rate of Increase of Wear-Land calculation can be explained with given input values -> 2097.051 = (0.0833333333333333*((2.66666666666667E-06*300/0.00032)^0.5))/(2*pi*10).

FAQ

What is Instantaneous Radius for Cut given Rate of Increase of Wear-Land?
The Instantaneous Radius for Cut given Rate of Increase of Wear-Land is a method to determine the maximum radius of the workpiece that can be machined on a given spindle speed when Rate of Increase of Wear-Land is given and is represented as r = (Vref*((dVBdtratio*Tref/VBm)^n))/(2*pi*ns) or Instantaneous Radius for Cut = (Reference Cutting Velocity*((Rate of Increase of Wear Land Width*Reference Tool Life/Maximum Wear Land Width)^Taylor's Tool Life Exponent))/(2*pi*Rotational Frequency of Spindle). Reference Cutting Velocity is the Cutting Velocity of the tool used in the reference Machining Condition, Rate of Increase of Wear Land Width is the increase in the width of the region where wear occurs in a tool per unit time, Reference Tool Life is the Tool Life of the tool obtained in the reference Machining Condition, Maximum Wear Land Width is the maximum width of the region where wear occurs in a tool, Taylor's Tool Life Exponent is an experimental exponent that helps in quantifying the rate of Tool Wear & Rotational Frequency of Spindle is the number of turns made by the spindle of the Machine for cutting in one second.
How to calculate Instantaneous Radius for Cut given Rate of Increase of Wear-Land?
The Instantaneous Radius for Cut given Rate of Increase of Wear-Land is a method to determine the maximum radius of the workpiece that can be machined on a given spindle speed when Rate of Increase of Wear-Land is given is calculated using Instantaneous Radius for Cut = (Reference Cutting Velocity*((Rate of Increase of Wear Land Width*Reference Tool Life/Maximum Wear Land Width)^Taylor's Tool Life Exponent))/(2*pi*Rotational Frequency of Spindle). To calculate Instantaneous Radius for Cut given Rate of Increase of Wear-Land, you need Reference Cutting Velocity (Vref), Rate of Increase of Wear Land Width (dVBdtratio), Reference Tool Life (Tref), Maximum Wear Land Width (VBm), Taylor's Tool Life Exponent (n) & Rotational Frequency of Spindle (ns). With our tool, you need to enter the respective value for Reference Cutting Velocity, Rate of Increase of Wear Land Width, Reference Tool Life, Maximum Wear Land Width, Taylor's Tool Life Exponent & Rotational Frequency of Spindle 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 Instantaneous Radius for Cut?
In this formula, Instantaneous Radius for Cut uses Reference Cutting Velocity, Rate of Increase of Wear Land Width, Reference Tool Life, Maximum Wear Land Width, Taylor's Tool Life Exponent & Rotational Frequency of Spindle. We can use 2 other way(s) to calculate the same, which is/are as follows -
  • Instantaneous Radius for Cut = Outside Radius of the Workpiece-Rotational Frequency of Spindle*Feed*Process Time
  • Instantaneous Radius for Cut = Cutting Velocity/(2*pi*Rotational Frequency of Spindle)
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