Reference Tool Life given Optimum Spindle Speed Solution

STEP 0: Pre-Calculation Summary
Formula Used
Reference Tool Life = (((Rotational Frequency of Spindle*2*pi*Outside Radius of the Workpiece/Reference Cutting Velocity)^(1/Taylor's Tool Life Exponent))*((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)))))/((1+Taylor's Tool Life Exponent)*Cost of a Tool*(1-Workpiece Radius Ratio))
Tref = (((ns*2*pi*ro/Vref)^(1/n))*((1-n)*(Ct*tc+Ct)*(1-(ar^((1+n)/n)))))/((1+n)*Ct*(1-ar))
This formula uses 1 Constants, 8 Variables
Constants Used
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
Variables Used
Reference Tool Life - (Measured in Second) - Reference Tool Life is the Tool Life of the tool obtained in the reference Machining Condition.
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.
Outside Radius of the Workpiece - (Measured in Meter) - Outside Radius of the Workpiece is the radius of the outermost surface of the workpiece, away from the machining tool.
Reference Cutting Velocity - (Measured in Meter per Second) - Reference Cutting Velocity is the Cutting Velocity of the tool used in the reference Machining Condition.
Taylor's Tool Life Exponent - Taylor's Tool Life Exponent is an experimental exponent that helps in quantifying the rate of Tool Wear.
Cost of a Tool - The Cost of a Tool is simply the cost of one tool being used for machining.
Time to Change One Tool - (Measured in Second) - Time to Change One Tool is the measure of time it takes to change one tool during machining.
Workpiece Radius Ratio - Workpiece Radius Ratio is the ratio of the inner radius of the workpiece to its outer radius.
STEP 1: Convert Input(s) to Base Unit
Rotational Frequency of Spindle: 10 Hertz --> 10 Hertz No Conversion Required
Outside Radius of the Workpiece: 1000 Millimeter --> 1 Meter (Check conversion here)
Reference Cutting Velocity: 5000 Millimeter per Minute --> 0.0833333333333333 Meter per Second (Check conversion here)
Taylor's Tool Life Exponent: 0.5 --> No Conversion Required
Cost of a Tool: 70 --> No Conversion Required
Time to Change One Tool: 0.6 Minute --> 36 Second (Check conversion here)
Workpiece Radius Ratio: 0.45 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Tref = (((ns*2*pi*ro/Vref)^(1/n))*((1-n)*(Ct*tc+Ct)*(1-(ar^((1+n)/n)))))/((1+n)*Ct*(1-ar)) --> (((10*2*pi*1/0.0833333333333333)^(1/0.5))*((1-0.5)*(70*36+70)*(1-(0.45^((1+0.5)/0.5)))))/((1+0.5)*70*(1-0.45))
Evaluating ... ...
Tref = 11586283.9121972
STEP 3: Convert Result to Output's Unit
11586283.9121972 Second -->193104.731869954 Minute (Check conversion here)
FINAL ANSWER
193104.731869954 193104.7 Minute <-- Reference Tool Life
(Calculation completed in 00.020 seconds)

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
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3 Reference Tool Life Calculators

Reference Tool Life given Optimum Spindle Speed
Go Reference Tool Life = (((Rotational Frequency of Spindle*2*pi*Outside Radius of the Workpiece/Reference Cutting Velocity)^(1/Taylor's Tool Life Exponent))*((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)))))/((1+Taylor's Tool Life Exponent)*Cost of a Tool*(1-Workpiece Radius Ratio))
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)))
Reference Tool Life given Cutting Speed for Constant-Cutting-Speed Operation
Go Reference Tool Life = ((Cutting Velocity/Reference Cutting Velocity)^(1/Taylor's Tool Life Exponent))*Time Proportion of Cutting Edge Engagement*Tool Life

Reference Tool Life given Optimum Spindle Speed Formula

Reference Tool Life = (((Rotational Frequency of Spindle*2*pi*Outside Radius of the Workpiece/Reference Cutting Velocity)^(1/Taylor's Tool Life Exponent))*((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)))))/((1+Taylor's Tool Life Exponent)*Cost of a Tool*(1-Workpiece Radius Ratio))
Tref = (((ns*2*pi*ro/Vref)^(1/n))*((1-n)*(Ct*tc+Ct)*(1-(ar^((1+n)/n)))))/((1+n)*Ct*(1-ar))

What is Reference Machining Condition?

Reference Machining Condition is usually a state of Machining Operation which has been idealized as the most suitable. It is used to draw a comparison between different other Machining Conditions.

How to Calculate Reference Tool Life given Optimum Spindle Speed?

Reference Tool Life given Optimum Spindle Speed calculator uses Reference Tool Life = (((Rotational Frequency of Spindle*2*pi*Outside Radius of the Workpiece/Reference Cutting Velocity)^(1/Taylor's Tool Life Exponent))*((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)))))/((1+Taylor's Tool Life Exponent)*Cost of a Tool*(1-Workpiece Radius Ratio)) to calculate the Reference Tool Life, The Reference Tool Life given Optimum Spindle Speed is a method to determine the tool Life of a Machining Tool when used under the reference condition such that the Facing Operation finishes at minimum expense. Reference Tool Life is denoted by Tref symbol.

How to calculate Reference Tool Life given Optimum Spindle Speed using this online calculator? To use this online calculator for Reference Tool Life given Optimum Spindle Speed, enter Rotational Frequency of Spindle (ns), Outside Radius of the Workpiece (ro), Reference Cutting Velocity (Vref), Taylor's Tool Life Exponent (n), Cost of a Tool (Ct), Time to Change One Tool (tc) & Workpiece Radius Ratio (ar) and hit the calculate button. Here is how the Reference Tool Life given Optimum Spindle Speed calculation can be explained with given input values -> 3218.412 = (((10*2*pi*1/0.0833333333333333)^(1/0.5))*((1-0.5)*(70*36+70)*(1-(0.45^((1+0.5)/0.5)))))/((1+0.5)*70*(1-0.45)) .

FAQ

What is Reference Tool Life given Optimum Spindle Speed?
The Reference Tool Life given Optimum Spindle Speed is a method to determine the tool Life of a Machining Tool when used under the reference condition such that the Facing Operation finishes at minimum expense and is represented as Tref = (((ns*2*pi*ro/Vref)^(1/n))*((1-n)*(Ct*tc+Ct)*(1-(ar^((1+n)/n)))))/((1+n)*Ct*(1-ar)) or Reference Tool Life = (((Rotational Frequency of Spindle*2*pi*Outside Radius of the Workpiece/Reference Cutting Velocity)^(1/Taylor's Tool Life Exponent))*((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)))))/((1+Taylor's Tool Life Exponent)*Cost of a Tool*(1-Workpiece Radius Ratio)). Rotational Frequency of Spindle is the number of turns made by the spindle of the Machine for cutting in one second, Outside Radius of the Workpiece is the radius of the outermost surface of the workpiece, away from the machining tool, Reference Cutting Velocity is the Cutting Velocity of the tool used in the reference Machining Condition, Taylor's Tool Life Exponent is an experimental exponent that helps in quantifying the rate of Tool Wear, The Cost of a Tool is simply the cost of one tool being used for machining, Time to Change One Tool is the measure of time it takes to change one tool during machining & Workpiece Radius Ratio is the ratio of the inner radius of the workpiece to its outer radius.
How to calculate Reference Tool Life given Optimum Spindle Speed?
The Reference Tool Life given Optimum Spindle Speed is a method to determine the tool Life of a Machining Tool when used under the reference condition such that the Facing Operation finishes at minimum expense is calculated using Reference Tool Life = (((Rotational Frequency of Spindle*2*pi*Outside Radius of the Workpiece/Reference Cutting Velocity)^(1/Taylor's Tool Life Exponent))*((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)))))/((1+Taylor's Tool Life Exponent)*Cost of a Tool*(1-Workpiece Radius Ratio)). To calculate Reference Tool Life given Optimum Spindle Speed, you need Rotational Frequency of Spindle (ns), Outside Radius of the Workpiece (ro), Reference Cutting Velocity (Vref), Taylor's Tool Life Exponent (n), Cost of a Tool (Ct), Time to Change One Tool (tc) & Workpiece Radius Ratio (ar). With our tool, you need to enter the respective value for Rotational Frequency of Spindle, Outside Radius of the Workpiece, Reference Cutting Velocity, Taylor's Tool Life Exponent, Cost of a Tool, Time to Change One Tool & Workpiece Radius Ratio 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 Reference Tool Life?
In this formula, Reference Tool Life uses Rotational Frequency of Spindle, Outside Radius of the Workpiece, Reference Cutting Velocity, Taylor's Tool Life Exponent, Cost of a Tool, Time to Change One Tool & Workpiece Radius Ratio. We can use 2 other way(s) to calculate the same, which is/are as follows -
  • Reference Tool Life = ((Cutting Velocity/Reference Cutting Velocity)^(1/Taylor's Tool Life Exponent))*Time Proportion of Cutting Edge Engagement*Tool Life
  • 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)))
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