Instantaneous Radius for Cut given Cutting Speed Calculator

✖The Cutting Velocity is the tangential velocity at the periphery of the cutter or workpiece (whichever is rotating).ⓘ Cutting Velocity [V]			+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 Cutting Speed [r]

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Formula

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Instantaneous Radius for Cut given Cutting Speed

Formula

`"r" = "V"/(2*pi*"n"_{"s"})`

Example

`"120mm"="452389.2mm/min"/(2*pi*"10Hz")`

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Instantaneous Radius for Cut given Cutting Speed Solution

STEP 0: Pre-Calculation Summary

Formula Used

Instantaneous Radius For Cut = Cutting Velocity/(2*pi*Rotational Frequency of Spindle)
r = V/(2*pi*n_s)
This formula uses 1 Constants, 3 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.
Cutting Velocity - (Measured in Meter per Second) - The Cutting Velocity is the tangential velocity at the periphery of the cutter or workpiece (whichever is rotating).
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

Cutting Velocity: 452389.2 Millimeter per Minute --> 7.53982 Meter per Second (Check conversion here)
Rotational Frequency of Spindle: 10 Hertz --> 10 Hertz No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r = V/(2*pi*n_s) --> 7.53982/(2*pi*10)

Evaluating ... ...

r = 0.119999962302313

STEP 3: Convert Result to Output's Unit

0.119999962302313 Meter -->119.999962302313 Millimeter (Check conversion here)

FINAL ANSWER

119.999962302313 ≈ 120 Millimeter <-- Instantaneous Radius For Cut

(Calculation completed in 00.004 seconds)

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

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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 Cutting Speed Formula

Instantaneous Radius For Cut = Cutting Velocity/(2*pi*Rotational Frequency of Spindle)
r = V/(2*pi*n_s)

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 Cutting Speed?

Instantaneous Radius for Cut given Cutting Speed calculator uses Instantaneous Radius For Cut = Cutting Velocity/(2*pi*Rotational Frequency of Spindle) to calculate the Instantaneous Radius For Cut, The Instantaneous Radius for Cut given Cutting Speed is a method to determine the maximum radius of the workpiece that can be machined on a given spindle speed such that the Instantaneous Cutting Speed is not disturbed. Instantaneous Radius For Cut is denoted by r symbol.

How to calculate Instantaneous Radius for Cut given Cutting Speed using this online calculator? To use this online calculator for Instantaneous Radius for Cut given Cutting Speed, enter Cutting Velocity (V) & Rotational Frequency of Spindle (n_s) and hit the calculate button. Here is how the Instantaneous Radius for Cut given Cutting Speed calculation can be explained with given input values -> 136000.3 = 7.53982/(2*pi*10).

FAQ

What is Instantaneous Radius for Cut given Cutting Speed?

The Instantaneous Radius for Cut given Cutting Speed is a method to determine the maximum radius of the workpiece that can be machined on a given spindle speed such that the Instantaneous Cutting Speed is not disturbed and is represented as r = V/(2*pi*n_s) or Instantaneous Radius For Cut = Cutting Velocity/(2*pi*Rotational Frequency of Spindle). The Cutting Velocity is the tangential velocity at the periphery of the cutter or workpiece (whichever is rotating) & 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 Cutting Speed?

The Instantaneous Radius for Cut given Cutting Speed is a method to determine the maximum radius of the workpiece that can be machined on a given spindle speed such that the Instantaneous Cutting Speed is not disturbed is calculated using Instantaneous Radius For Cut = Cutting Velocity/(2*pi*Rotational Frequency of Spindle). To calculate Instantaneous Radius for Cut given Cutting Speed, you need Cutting Velocity (V) & Rotational Frequency of Spindle (n_s). With our tool, you need to enter the respective value for Cutting Velocity & 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 Cutting Velocity & Rotational Frequency of Spindle. We can use 2 other way(s) to calculate the same, which is/are as follows -

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 = Outside Radius of The Workpiece-Rotational Frequency of Spindle*Feed*Process Time

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