Rotational Frequency of Spindle 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 [W_max]			+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%
✖Instantaneous Radius For Cut is the radius of the workpiece surface currently being machined.ⓘ Instantaneous Radius For Cut [r]			+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 given Rate of Increase of Wear-Land [n_s]

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Formula

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

Formula

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

Example

`"10Hz"=("5000mm/min"*(("0.16mm/min"*"5min"/"0.3125mm")^"0.5"))/(2*pi*"2.122065mm")`

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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)
n_s = (V_ref*((V_ratio*T_ref/W_max)^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: 0.3125 Millimeter --> 0.0003125 Meter (Check conversion here)
Taylor's Tool Life Exponent: 0.5 --> No Conversion Required
Instantaneous Radius For Cut: 2.122065 Millimeter --> 0.002122065 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

n_s = (V_ref*((V_ratio*T_ref/W_max)^n))/(2*pi*r) --> (0.0833333333333333*((2.66666666666667E-06*300/0.0003125)^0.5))/(2*pi*0.002122065)

Evaluating ... ...

n_s = 10.0000042783418

STEP 3: Convert Result to Output's Unit

10.0000042783418 Hertz --> No Conversion Required

FINAL ANSWER

10.0000042783418 ≈ 10 Hertz <-- Rotational Frequency of Spindle

(Calculation completed in 00.004 seconds)

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Credits

Created by Kumar Siddhant

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

Kumar Siddhant has created this Calculator and 400+ more calculators!

Verified by Parul Keshav

National Institute of Technology (NIT), Srinagar

Parul Keshav has verified this Calculator and 400+ more calculators!

< 13 Wear Land Calculators

Rate of Increase of Wear-Land given Feed and Time for Facing

Go Rate of Increase of Wear Land Width = Maximum Wear Land Width/(Reference Tool Life*((Reference Cutting Velocity/(2*pi*Rotational Frequency of Spindle*(Outside Radius of The Workpiece-Rotational Frequency of Spindle*Feed*Process Time)))^(1/Taylor's Tool Life Exponent)))

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

Go Rate of Increase of Wear Land Width = Maximum Wear Land Width/(Reference Tool Life*((Reference Cutting Velocity/(2*pi*Rotational Frequency of Spindle*Instantaneous Radius For Cut))^(1/Taylor's Tool Life Exponent)))

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)

Increase in Wear-Land Width given Rate of Increase of Wear-Land Width

Go Increase in Wear Land Width Per Component = Machining Time*Rate of Increase of Wear Land Width*Reference Tool Life*((Reference Cutting Velocity/Cutting Velocity)^(1/Taylor's Tool Life Exponent))/Tool Life

Tool Life given Rate of Increase of Wear-Land Width

Go Tool Life = Machining Time*Rate of Increase of Wear Land Width*Reference Tool Life*((Reference Cutting Velocity/Cutting Velocity)^(1/Taylor's Tool Life Exponent))/Increase in Wear Land Width Per Component

Tool Life Exponent given Rate of Increase of Wear-Land Width

Go Taylor's Tool Life Exponent = ln(Reference Cutting Velocity/Cutting Velocity)/ln(Maximum Wear Land Width/(Rate of Increase of Wear Land Width*Reference Tool Life))

Reference Tool Life given Rate of Increase of Wear-Land Width

Go Reference Tool Life = Maximum Wear Land Width/(Rate of Increase of Wear Land Width*((Reference Cutting Velocity/Cutting Velocity)^(1/Taylor's Tool Life Exponent)))

Rate of Increase of Wear-Land Width

Go Rate of Increase of Wear Land Width = Maximum Wear Land Width/(Reference Tool Life*((Reference Cutting Velocity/Cutting Velocity)^(1/Taylor's Tool Life Exponent)))

Maximum Wear-Land Width given Rate of Increase of Wear-Land Width

Go Maximum Wear Land Width = Rate of Increase of Wear Land Width*Reference Tool Life*((Reference Cutting Velocity/Cutting Velocity)^(1/Taylor's Tool Life Exponent))

Machining Time given Maximum Wear-Land Width

Go Machining Time = Increase in Wear Land Width Per Component*Tool Life/Maximum Wear Land Width

Increase in Wear-Land Width per Component

Go Increase in Wear Land Width Per Component = Maximum Wear Land Width*Machining Time/Tool Life

Tool Life given Maximum Wear-Land Width

Go Tool Life = Maximum Wear Land Width*Machining Time/Increase in Wear Land Width Per Component

Maximum Wear-Land Width

Go Maximum Wear Land Width = Increase in Wear Land Width Per Component*Tool Life/Machining Time

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

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 n_s 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 (V_ref), Rate of Increase of Wear Land Width (V_ratio), Reference Tool Life (T_ref), Maximum Wear Land Width (W_max), 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 -> 0.155948 = (0.0833333333333333*((2.66666666666667E-06*300/0.0003125)^0.5))/(2*pi*0.002122065).

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 n_s = (V_ref*((V_ratio*T_ref/W_max)^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 (V_ref), Rate of Increase of Wear Land Width (V_ratio), Reference Tool Life (T_ref), Maximum Wear Land Width (W_max), 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.

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