Rotational Frequency of Spindle given Rate of Increase of Wear-Land Solution

STEP 0: Pre-Calculation Summary
Formula Used
Rotational Frequency of Spindle = (Reference Cutting Velocity*((Rate of Increase of Wear Land Width*Reference Tool Life/Maximum Wear Land Width)^Taylor's Tool Life Exponent))/(2*pi*Instantaneous Radius for Cut)
ns = (Vref*((dVBdtratio*Tref/VBm)^n))/(2*pi*r)
This formula uses 1 Constants, 7 Variables
Constants Used
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
Variables Used
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.
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.
Instantaneous Radius for Cut - (Measured in Meter) - Instantaneous Radius for Cut is the radius of the workpiece surface currently being machined.
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
Instantaneous Radius for Cut: 120 Millimeter --> 0.12 Meter (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
ns = (Vref*((dVBdtratio*Tref/VBm)^n))/(2*pi*r) --> (0.0833333333333333*((2.66666666666667E-06*300/0.00032)^0.5))/(2*pi*0.12)
Evaluating ... ...
ns = 0.174754208696136
STEP 3: Convert Result to Output's Unit
0.174754208696136 Hertz --> No Conversion Required
FINAL ANSWER
0.174754208696136 0.174754 Hertz <-- Rotational Frequency of Spindle
(Calculation completed in 00.004 seconds)

Credits

Created by Kumar Siddhant
Indian Institute of Information Technology, Design and Manufacturing (IIITDM), Jabalpur
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4 Rotational Frequency Calculators

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

Rotational Frequency of Spindle given Rate of Increase of Wear-Land Formula

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

Main Spindle Errors

Accuracy of spindle error measurement is affected by inherent error sources such as:
1. Sensor offset
2. Thermal drift of spindle
3. Centering error
4. Form error of the target surface installed in the spindle.

How to Calculate Rotational Frequency of Spindle given Rate of Increase of Wear-Land?

Rotational Frequency of Spindle given Rate of Increase of Wear-Land calculator uses Rotational Frequency of Spindle = (Reference Cutting Velocity*((Rate of Increase of Wear Land Width*Reference Tool Life/Maximum Wear Land Width)^Taylor's Tool Life Exponent))/(2*pi*Instantaneous Radius for Cut) to calculate the Rotational Frequency of Spindle, The Rotational Frequency of Spindle given Rate of Increase of Wear-Land is a method to determine the required frequency of rotation of the Spindle of a Machining Tool when the Rate of Increase of Wear-Land Width is given. Rotational Frequency of Spindle is denoted by ns symbol.

How to calculate Rotational Frequency of Spindle given Rate of Increase of Wear-Land using this online calculator? To use this online calculator for Rotational Frequency of Spindle 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) & Instantaneous Radius for Cut (r) and hit the calculate button. Here is how the Rotational Frequency of Spindle given Rate of Increase of Wear-Land calculation can be explained with given input values -> 0.174754 = (0.0833333333333333*((2.66666666666667E-06*300/0.00032)^0.5))/(2*pi*0.12) .

FAQ

What is Rotational Frequency of Spindle given Rate of Increase of Wear-Land?
The Rotational Frequency of Spindle given Rate of Increase of Wear-Land is a method to determine the required frequency of rotation of the Spindle of a Machining Tool when the Rate of Increase of Wear-Land Width is given and is represented as ns = (Vref*((dVBdtratio*Tref/VBm)^n))/(2*pi*r) or Rotational Frequency of Spindle = (Reference Cutting Velocity*((Rate of Increase of Wear Land Width*Reference Tool Life/Maximum Wear Land Width)^Taylor's Tool Life Exponent))/(2*pi*Instantaneous Radius for Cut). 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 & Instantaneous Radius for Cut is the radius of the workpiece surface currently being machined.
How to calculate Rotational Frequency of Spindle given Rate of Increase of Wear-Land?
The Rotational Frequency of Spindle given Rate of Increase of Wear-Land is a method to determine the required frequency of rotation of the Spindle of a Machining Tool when the Rate of Increase of Wear-Land Width is given is calculated using Rotational Frequency of Spindle = (Reference Cutting Velocity*((Rate of Increase of Wear Land Width*Reference Tool Life/Maximum Wear Land Width)^Taylor's Tool Life Exponent))/(2*pi*Instantaneous Radius for Cut). To calculate Rotational Frequency of Spindle 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) & Instantaneous Radius for Cut (r). 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 & Instantaneous Radius for Cut 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 Rotational Frequency of Spindle?
In this formula, Rotational Frequency of Spindle uses Reference Cutting Velocity, Rate of Increase of Wear Land Width, Reference Tool Life, Maximum Wear Land Width, Taylor's Tool Life Exponent & Instantaneous Radius for Cut. We can use 3 other way(s) to calculate the same, which is/are as follows -
  • Rotational Frequency of Spindle = Cutting Velocity/(2*pi*Instantaneous Radius for Cut)
  • Rotational Frequency of Spindle = (Outside Radius of the Workpiece-Instantaneous Radius for Cut)/(Process Time*Feed)
  • Rotational Frequency of Spindle = (Outside Radius of the Workpiece-Inner Radius of Workpiece)/(Machining Time*Feed)
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