Reference Cutting Velocity given Optimum Spindle Speed Solution

STEP 0: Pre-Calculation Summary
Formula Used
Reference Cutting Velocity = Rotational Frequency of Spindle*2*pi*Outside Radius of the Workpiece/((((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)
Vref = ns*2*pi*ro/((((1+n)*Ct*Tref*(1-ar))/((1-n)*(Ct*tc+Ct)*(1-(ar^((1+n)/n)))))^n)
This formula uses 1 Constants, 8 Variables
Constants Used
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
Variables Used
Reference Cutting Velocity - (Measured in Meter per Second) - Reference Cutting Velocity is the Cutting Velocity of the tool used 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.
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.
Reference Tool Life - (Measured in Second) - Reference Tool Life is the Tool Life of the tool obtained in the reference Machining Condition.
Workpiece Radius Ratio - Workpiece Radius Ratio is the ratio of the inner radius of the workpiece to its outer radius.
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.
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)
Taylor's Tool Life Exponent: 0.5 --> No Conversion Required
Cost of a Tool: 70 --> No Conversion Required
Reference Tool Life: 5 Minute --> 300 Second (Check conversion here)
Workpiece Radius Ratio: 0.45 --> No Conversion Required
Time to Change One Tool: 0.6 Minute --> 36 Second (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Vref = ns*2*pi*ro/((((1+n)*Ct*Tref*(1-ar))/((1-n)*(Ct*tc+Ct)*(1-(ar^((1+n)/n)))))^n) --> 10*2*pi*1/((((1+0.5)*70*300*(1-0.45))/((1-0.5)*(70*36+70)*(1-(0.45^((1+0.5)/0.5)))))^0.5)
Evaluating ... ...
Vref = 16.3768439110241
STEP 3: Convert Result to Output's Unit
16.3768439110241 Meter per Second -->982610.634661446 Millimeter per Minute (Check conversion here)
FINAL ANSWER
982610.634661446 982610.6 Millimeter per Minute <-- Reference Cutting Velocity
(Calculation completed in 00.004 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
Parul Keshav has verified this Calculator and 400+ more calculators!

7 Cutting Velocity Calculators

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

Reference Cutting Velocity given Optimum Spindle Speed Formula

Reference Cutting Velocity = Rotational Frequency of Spindle*2*pi*Outside Radius of the Workpiece/((((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)
Vref = ns*2*pi*ro/((((1+n)*Ct*Tref*(1-ar))/((1-n)*(Ct*tc+Ct)*(1-(ar^((1+n)/n)))))^n)

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 Cutting Velocity given Optimum Spindle Speed?

Reference Cutting Velocity given Optimum Spindle Speed calculator uses Reference Cutting Velocity = Rotational Frequency of Spindle*2*pi*Outside Radius of the Workpiece/((((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) to calculate the Reference Cutting Velocity, The Reference Cutting Velocity given Optimum Spindle Speed is a method to determine the Cutting Velocity for the reference condition when the Facing Operation has to be finished at minimum expense. Reference Cutting Velocity is denoted by Vref symbol.

How to calculate Reference Cutting Velocity given Optimum Spindle Speed using this online calculator? To use this online calculator for Reference Cutting Velocity given Optimum Spindle Speed, enter Rotational Frequency of Spindle (ns), Outside Radius of the Workpiece (ro), Taylor's Tool Life Exponent (n), Cost of a Tool (Ct), Reference Tool Life (Tref), Workpiece Radius Ratio (ar) & Time to Change One Tool (tc) and hit the calculate button. Here is how the Reference Cutting Velocity given Optimum Spindle Speed calculation can be explained with given input values -> 5.9E+10 = 10*2*pi*1/((((1+0.5)*70*300*(1-0.45))/((1-0.5)*(70*36+70)*(1-(0.45^((1+0.5)/0.5)))))^0.5).

FAQ

What is Reference Cutting Velocity given Optimum Spindle Speed?
The Reference Cutting Velocity given Optimum Spindle Speed is a method to determine the Cutting Velocity for the reference condition when the Facing Operation has to be finished at minimum expense and is represented as Vref = ns*2*pi*ro/((((1+n)*Ct*Tref*(1-ar))/((1-n)*(Ct*tc+Ct)*(1-(ar^((1+n)/n)))))^n) or Reference Cutting Velocity = Rotational Frequency of Spindle*2*pi*Outside Radius of the Workpiece/((((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). 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, 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, Reference Tool Life is the Tool Life of the tool obtained in the reference Machining Condition, Workpiece Radius Ratio is the ratio of the inner radius of the workpiece to its outer radius & Time to Change One Tool is the measure of time it takes to change one tool during machining.
How to calculate Reference Cutting Velocity given Optimum Spindle Speed?
The Reference Cutting Velocity given Optimum Spindle Speed is a method to determine the Cutting Velocity for the reference condition when the Facing Operation has to be finished at minimum expense is calculated using Reference Cutting Velocity = Rotational Frequency of Spindle*2*pi*Outside Radius of the Workpiece/((((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). To calculate Reference Cutting Velocity given Optimum Spindle Speed, you need Rotational Frequency of Spindle (ns), Outside Radius of the Workpiece (ro), Taylor's Tool Life Exponent (n), Cost of a Tool (Ct), Reference Tool Life (Tref), Workpiece Radius Ratio (ar) & Time to Change One Tool (tc). With our tool, you need to enter the respective value for Rotational Frequency of Spindle, Outside Radius of the Workpiece, Taylor's Tool Life Exponent, Cost of a Tool, Reference Tool Life, Workpiece Radius Ratio & Time to Change One Tool 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 Cutting Velocity?
In this formula, Reference Cutting Velocity uses Rotational Frequency of Spindle, Outside Radius of the Workpiece, Taylor's Tool Life Exponent, Cost of a Tool, Reference Tool Life, Workpiece Radius Ratio & Time to Change One Tool. We can use 2 other way(s) to calculate the same, which is/are as follows -
  • Reference Cutting Velocity = Cutting Velocity/((Reference Tool Life/(Tool Life*Time Proportion of Cutting Edge Engagement))^Taylor's Tool Life Exponent)
  • Reference Cutting Velocity = Cutting Velocity/((Rate of Increase of Wear Land Width*Reference Tool Life/Maximum Wear Land Width)^Taylor's Tool Life Exponent)
Let Others Know
Facebook
Twitter
Reddit
LinkedIn
Email
WhatsApp
Copied!