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

✖Reference Cutting Velocity is the Cutting Velocity of the tool used in the reference Machining Condition.ⓘ Reference Cutting Velocity [V_ref]			+10% -10%
✖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.ⓘ Rate of Increase of Wear Land Width [V_ratio]			+10% -10%
✖Reference Tool Life is the Tool Life of the tool obtained in the reference Machining Condition.ⓘ Reference Tool Life [T_ref]			+10% -10%
✖Maximum Wear Land Width is the maximum width of the region where wear occurs in a tool.ⓘ Maximum Wear Land Width [VB_m]			+10% -10%
✖Taylor's Tool Life Exponent is an experimental exponent that helps in quantifying the rate of Tool Wear.ⓘ Taylor's Tool Life Exponent [n]			+10% -10%
✖Rotational Frequency of Spindle is the number of turns made by the spindle of the Machine for cutting in one second.ⓘ Rotational Frequency of Spindle [n_s]			+10% -10%

✖Instantaneous Radius for Cut is the radius of the workpiece surface currently being machined.ⓘ Instantaneous Radius for Cut given Rate of Increase of Wear-Land [r]

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Formula

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

Formula

`"r" = ("V"_{"ref"}*(("V"_{"ratio"}*"T"_{"ref"}/"VB"_{"m"})^"n"))/(2*pi*"n"_{"s"})`

Example

`"114.5521mm"=("1.050061E^6mm/min"*(("543.503mm/min"*"5min"/"16066.91mm")^"0.5"))/(2*pi*"10Hz")`

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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 = (V_ref*((V_ratio*T_ref/VB_m)^n))/(2*pi*n_s)
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: 1050061 Millimeter per Minute --> 17.5010166666667 Meter per Second (Check conversion here)
Rate of Increase of Wear Land Width: 543.503 Millimeter per Minute --> 0.00905838333333333 Meter per Second (Check conversion here)
Reference Tool Life: 5 Minute --> 300 Second (Check conversion here)
Maximum Wear Land Width: 16066.91 Millimeter --> 16.06691 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 = (V_ref*((V_ratio*T_ref/VB_m)^n))/(2*pi*n_s) --> (17.5010166666667*((0.00905838333333333*300/16.06691)^0.5))/(2*pi*10)

Evaluating ... ...

r = 0.114552139389794

STEP 3: Convert Result to Output's Unit

0.114552139389794 Meter -->114.552139389794 Millimeter (Check conversion here)

FINAL ANSWER

114.552139389794 ≈ 114.5521 Millimeter <-- Instantaneous Radius For Cut

(Calculation completed in 00.004 seconds)

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Created by Kumar Siddhant

Indian Institute of Information Technology, Design and Manufacturing (IIITDM), Jabalpur

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Verified by Parul Keshav

National Institute of Technology (NIT), Srinagar

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< 11 Instantaneous Radius Calculators

Outside Radius of Workpiece given Optimum Spindle Speed

Go Outside Radius of The Workpiece = (Reference Cutting Velocity/(2*pi*Rotational Frequency of Spindle))*((((1+Taylor's Tool Life Exponent)*Cost of A Tool*Reference Tool Life*(1-Workpiece Radius Ratio))/((1-Taylor's Tool Life Exponent)*(Cost of A Tool*Time to Change One Tool+Cost of A Tool)*(1-(Workpiece Radius Ratio^((1+Taylor's Tool Life Exponent)/Taylor's Tool Life Exponent)))))^Taylor's Tool Life Exponent)

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)

Outside Radius of Workpiece given Instantaneous Cutting Speed

Go Outside Radius of The Workpiece = (Cutting Velocity/(2*pi*Rotational Frequency of Spindle))+Rotational Frequency of Spindle*Feed*Process Time

Rotational Frequency of Spindle given Instantaneous Radius for Cut

Go Rotational Frequency of Spindle = (Outside Radius of The Workpiece-Instantaneous Radius For Cut)/(Process Time*Feed)

Feed given Instantaneous Radius for Cut

Go Feed = (Outside Radius of The Workpiece-Instantaneous Radius For Cut)/(Rotational Frequency of Spindle*Process Time)

Outside Radius of Workpiece given Instantaneous Radius for Cut

Go Outside Radius of The Workpiece = Instantaneous Radius For Cut+Rotational Frequency of Spindle*Feed*Process Time

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)

Outside Radius given Workpiece Radius Ratio

Go Outside Radius of The Workpiece = Inner Radius of Workpiece/Workpiece Radius Ratio

Inside Radius given Workpiece Radius Ratio

Go Inner Radius of Workpiece = Workpiece Radius Ratio*Outside Radius of The Workpiece

Workpiece Radius Ratio

Go Workpiece Radius Ratio = Inner Radius of Workpiece/Outside Radius of The Workpiece

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

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 (V_ref), Rate of Increase of Wear Land Width (V_ratio), Reference Tool Life (T_ref), Maximum Wear Land Width (VB_m), Taylor's Tool Life Exponent (n) & Rotational Frequency of Spindle (n_s) 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 -> 2.5E+7 = (17.5010166666667*((0.00905838333333333*300/16.06691)^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 = (V_ref*((V_ratio*T_ref/VB_m)^n))/(2*pi*n_s) 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 (V_ref), Rate of Increase of Wear Land Width (V_ratio), Reference Tool Life (T_ref), Maximum Wear Land Width (VB_m), Taylor's Tool Life Exponent (n) & Rotational Frequency of Spindle (n_s). 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 = Cutting Velocity/(2*pi*Rotational Frequency of Spindle)
Instantaneous Radius For Cut = Outside Radius of The Workpiece-Rotational Frequency of Spindle*Feed*Process Time

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