Cost of 1 Tool given Optimum Spindle Speed Solution

STEP 0: Pre-Calculation Summary
Formula Used
Cost of a Tool = (Machining and Operating Rate*(((((((Reference Cutting Velocity/(2*pi*Outside Radius of the Workpiece)))/Rotational Frequency of Spindle)^(1/Taylor's Tool Life Exponent))*((((1+Taylor's Tool Life Exponent)/(1-Taylor's Tool Life Exponent)))*((1-Workpiece Radius Ratio)/(1-((Workpiece Radius Ratio)^((Taylor's Tool Life Exponent+1)/Taylor's Tool Life Exponent))))*Maximum Tool Life))))-Time to Change One Tool)
Ct = (M*(((((((Vref/(2*pi*ro)))/ns)^(1/n))*((((1+n)/(1-n)))*((1-ar)/(1-((ar)^((n+1)/n))))*Tmax))))-tc)
This formula uses 1 Constants, 9 Variables
Constants Used
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
Variables Used
Cost of a Tool - The Cost of a Tool is simply the cost of one tool being used for machining.
Machining and Operating Rate - Machining and Operating Rate is the money charged for processing on and operating machines per unit time, including overheads.
Reference Cutting Velocity - (Measured in Meter per Second) - Reference Cutting Velocity is the Cutting Velocity of the tool used in the reference Machining Condition.
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.
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.
Taylor's Tool Life Exponent - Taylor's Tool Life Exponent is an experimental exponent that helps in quantifying the rate of Tool Wear.
Workpiece Radius Ratio - Workpiece Radius Ratio is the ratio of the inner radius of the workpiece to its outer radius.
Maximum Tool Life - (Measured in Second) - Maximum Tool Life is the Tool Life of the tool obtained in the reference Machining Condition.
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
Machining and Operating Rate: 100 --> No Conversion Required
Reference Cutting Velocity: 5000 Millimeter per Minute --> 0.0833333333333333 Meter per Second (Check conversion here)
Outside Radius of the Workpiece: 1000 Millimeter --> 1 Meter (Check conversion here)
Rotational Frequency of Spindle: 10 Hertz --> 10 Hertz No Conversion Required
Taylor's Tool Life Exponent: 0.5 --> No Conversion Required
Workpiece Radius Ratio: 0.45 --> No Conversion Required
Maximum Tool Life: 7000 Minute --> 420000 Second (Check conversion here)
Time to Change One Tool: 0.6 Minute --> 36 Second (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Ct = (M*(((((((Vref/(2*pi*ro)))/ns)^(1/n))*((((1+n)/(1-n)))*((1-ar)/(1-((ar)^((n+1)/n))))*Tmax))))-tc) --> (100*(((((((0.0833333333333333/(2*pi*1)))/10)^(1/0.5))*((((1+0.5)/(1-0.5)))*((1-0.45)/(1-((0.45)^((0.5+1)/0.5))))*420000))))-36)
Evaluating ... ...
Ct = 98.1241084524138
STEP 3: Convert Result to Output's Unit
98.1241084524138 --> No Conversion Required
FINAL ANSWER
98.1241084524138 98.12411 <-- Cost of a Tool
(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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19 Facing Operation Calculators

Optimum Spindle Speed
Go Rotational Frequency of Spindle = (Reference Cutting Velocity/(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)
Machining and Operating Rate given Optimum Spindle Speed
Go Machining and Operating Rate = (Cost of a Tool/(((((((Reference Cutting Velocity/(2*pi*Outside Radius of the Workpiece)))/Rotational Frequency of Spindle)^(1/Taylor's Tool Life Exponent))*((((1+Taylor's Tool Life Exponent)/(1-Taylor's Tool Life Exponent)))*((1-Workpiece Radius Ratio)/(1-((Workpiece Radius Ratio)^((Taylor's Tool Life Exponent+1)/Taylor's Tool Life Exponent))))*Reference Tool Life))))-Time to Change One Tool)
Cost of 1 Tool given Optimum Spindle Speed
Go Cost of a Tool = (Machining and Operating Rate*(((((((Reference Cutting Velocity/(2*pi*Outside Radius of the Workpiece)))/Rotational Frequency of Spindle)^(1/Taylor's Tool Life Exponent))*((((1+Taylor's Tool Life Exponent)/(1-Taylor's Tool Life Exponent)))*((1-Workpiece Radius Ratio)/(1-((Workpiece Radius Ratio)^((Taylor's Tool Life Exponent+1)/Taylor's Tool Life Exponent))))*Maximum Tool Life))))-Time to Change One Tool)
Optimum Spindle Speed given Tool Changing Cost
Go Rotational Frequency of Spindle = (Reference Cutting Velocity/(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 changing each 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)
Tool Changing Time given Optimum Spindle Speed
Go Time to Change One Tool = Reference Tool Life/((Rotational Frequency of Spindle*2*pi*Outer Radius of Workpiece/Reference Cutting Velocity)^(1/Taylor's Tool Life Exponent)*(1-Workpiece Radius Ratio^((1+Taylor's Tool Life Exponent)/Taylor's Tool Life Exponent))*(1-Taylor's Tool Life Exponent)/((1+Taylor's Tool Life Exponent)*(1-Workpiece Radius Ratio)))-Cost of a Tool/Machining and Operating Rate
Tool Changing Cost given Optimum Spindle Speed
Go Cost of changing each Tool = (Cost of a Tool*Maximum Tool Life/(((Rotational Frequency of Spindle*2*pi*Outside Radius of the Workpiece/Reference Cutting Velocity)^(1/Taylor's Tool Life Exponent))*(1-(Workpiece Radius Ratio^((1+Taylor's Tool Life Exponent)/Taylor's Tool Life Exponent)))*(1-Taylor's Tool Life Exponent)/((1+Taylor's Tool Life Exponent)*(1-Workpiece Radius Ratio))))-Cost of a Tool
Machining Time given Rate of Increase of Wear-Land Width
Go Machining Time = Tool Life/(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)
Taylor's Exponent given Cutting Speed for Constant-Cutting-Speed Operation
Go Taylor's Tool Life Exponent = ln(Cutting Velocity/Reference Cutting Velocity)/ln(Maximum Tool Life/(Tool Life*Time Proportion of Cutting Edge Engagement))
Time for Facing given Instantaneous Cutting Speed
Go Process Time = (Outside Radius of the Workpiece-(Cutting Velocity/(2*pi*Rotational Frequency of Spindle)))/(Rotational Frequency of Spindle*Feed)
Feed given Instantaneous Cutting Speed
Go Feed = (Outside Radius of the Workpiece-(Cutting Velocity/(2*pi*Rotational Frequency of Spindle)))/(Rotational Frequency of Spindle*Process Time)
Time Proportion of Edge Engagement given Cutting Speed for Constant-Cutting-Speed Operation
Go Time Proportion of Cutting Edge Engagement = Reference Tool Life*((Reference Cutting Velocity/Cutting Velocity)^(1/Taylor's Tool Life Exponent))/Tool Life
Feed of Workpiece given Machining Time for Facing
Go Feed = (Outside Radius of the Workpiece-Inner Radius of Workpiece)/(Rotational Frequency of Spindle*Machining Time)
Total Machining Time for single Facing Operation
Go Machining Time = (Outside Radius of the Workpiece-Inner Radius of Workpiece)/(Rotational Frequency of Spindle*Feed)
Feed given Instantaneous Radius for Cut
Go Feed = (Outside Radius of the Workpiece-Instantaneous Radius for Cut)/(Rotational Frequency of Spindle*Process Time)
Time for Facing
Go Process Time = (Outside Radius of the Workpiece-Instantaneous Radius for Cut)/(Rotational Frequency of Spindle*Feed)
Inner Radius of Workpiece given Machining Time for Facing
Go Inner Radius of Workpiece = Outside Radius of the Workpiece-Rotational Frequency of Spindle*Feed*Machining Time
Machining Time given Maximum Wear-Land Width
Go Machining Time = Increase in Wear Land Width per Component*Tool Life/Maximum Wear Land Width
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

Cost of 1 Tool given Optimum Spindle Speed Formula

Cost of a Tool = (Machining and Operating Rate*(((((((Reference Cutting Velocity/(2*pi*Outside Radius of the Workpiece)))/Rotational Frequency of Spindle)^(1/Taylor's Tool Life Exponent))*((((1+Taylor's Tool Life Exponent)/(1-Taylor's Tool Life Exponent)))*((1-Workpiece Radius Ratio)/(1-((Workpiece Radius Ratio)^((Taylor's Tool Life Exponent+1)/Taylor's Tool Life Exponent))))*Maximum Tool Life))))-Time to Change One Tool)
Ct = (M*(((((((Vref/(2*pi*ro)))/ns)^(1/n))*((((1+n)/(1-n)))*((1-ar)/(1-((ar)^((n+1)/n))))*Tmax))))-tc)

Significance of Cost of Tools Used

The Cost of Tools Used helps us in determining the maximum number of times a tool can be renewed during the production of a given batch of products. This renewing might include buying or resharpening the tool. Thus if the number of Tools to be used gets bounded, the machining operation would have to be optimized in order to give sufficient tool life to minimize the Total Cost of Production.

How to Calculate Cost of 1 Tool given Optimum Spindle Speed?

Cost of 1 Tool given Optimum Spindle Speed calculator uses Cost of a Tool = (Machining and Operating Rate*(((((((Reference Cutting Velocity/(2*pi*Outside Radius of the Workpiece)))/Rotational Frequency of Spindle)^(1/Taylor's Tool Life Exponent))*((((1+Taylor's Tool Life Exponent)/(1-Taylor's Tool Life Exponent)))*((1-Workpiece Radius Ratio)/(1-((Workpiece Radius Ratio)^((Taylor's Tool Life Exponent+1)/Taylor's Tool Life Exponent))))*Maximum Tool Life))))-Time to Change One Tool) to calculate the Cost of a Tool, The Cost of 1 Tool given Optimum Spindle Speed is a method to determine the maximum amount available to be spent on renewing the Machining Tool, such that the Production Cost is Minimum. Cost of a Tool is denoted by Ct symbol.

How to calculate Cost of 1 Tool given Optimum Spindle Speed using this online calculator? To use this online calculator for Cost of 1 Tool given Optimum Spindle Speed, enter Machining and Operating Rate (M), Reference Cutting Velocity (Vref), Outside Radius of the Workpiece (ro), Rotational Frequency of Spindle (ns), Taylor's Tool Life Exponent (n), Workpiece Radius Ratio (ar), Maximum Tool Life (Tmax) & Time to Change One Tool (tc) and hit the calculate button. Here is how the Cost of 1 Tool given Optimum Spindle Speed calculation can be explained with given input values -> -35.904197 = (100*(((((((0.0833333333333333/(2*pi*1)))/10)^(1/0.5))*((((1+0.5)/(1-0.5)))*((1-0.45)/(1-((0.45)^((0.5+1)/0.5))))*420000))))-36).

FAQ

What is Cost of 1 Tool given Optimum Spindle Speed?
The Cost of 1 Tool given Optimum Spindle Speed is a method to determine the maximum amount available to be spent on renewing the Machining Tool, such that the Production Cost is Minimum and is represented as Ct = (M*(((((((Vref/(2*pi*ro)))/ns)^(1/n))*((((1+n)/(1-n)))*((1-ar)/(1-((ar)^((n+1)/n))))*Tmax))))-tc) or Cost of a Tool = (Machining and Operating Rate*(((((((Reference Cutting Velocity/(2*pi*Outside Radius of the Workpiece)))/Rotational Frequency of Spindle)^(1/Taylor's Tool Life Exponent))*((((1+Taylor's Tool Life Exponent)/(1-Taylor's Tool Life Exponent)))*((1-Workpiece Radius Ratio)/(1-((Workpiece Radius Ratio)^((Taylor's Tool Life Exponent+1)/Taylor's Tool Life Exponent))))*Maximum Tool Life))))-Time to Change One Tool). Machining and Operating Rate is the money charged for processing on and operating machines per unit time, including overheads, Reference Cutting Velocity is the Cutting Velocity of the tool used in the reference Machining Condition, Outside Radius of the Workpiece is the radius of the outermost surface of the workpiece, away from the machining tool, Rotational Frequency of Spindle is the number of turns made by the spindle of the Machine for cutting in one second, Taylor's Tool Life Exponent is an experimental exponent that helps in quantifying the rate of Tool Wear, Workpiece Radius Ratio is the ratio of the inner radius of the workpiece to its outer radius, Maximum Tool Life is the Tool Life of the tool obtained in the reference Machining Condition & Time to Change One Tool is the measure of time it takes to change one tool during machining.
How to calculate Cost of 1 Tool given Optimum Spindle Speed?
The Cost of 1 Tool given Optimum Spindle Speed is a method to determine the maximum amount available to be spent on renewing the Machining Tool, such that the Production Cost is Minimum is calculated using Cost of a Tool = (Machining and Operating Rate*(((((((Reference Cutting Velocity/(2*pi*Outside Radius of the Workpiece)))/Rotational Frequency of Spindle)^(1/Taylor's Tool Life Exponent))*((((1+Taylor's Tool Life Exponent)/(1-Taylor's Tool Life Exponent)))*((1-Workpiece Radius Ratio)/(1-((Workpiece Radius Ratio)^((Taylor's Tool Life Exponent+1)/Taylor's Tool Life Exponent))))*Maximum Tool Life))))-Time to Change One Tool). To calculate Cost of 1 Tool given Optimum Spindle Speed, you need Machining and Operating Rate (M), Reference Cutting Velocity (Vref), Outside Radius of the Workpiece (ro), Rotational Frequency of Spindle (ns), Taylor's Tool Life Exponent (n), Workpiece Radius Ratio (ar), Maximum Tool Life (Tmax) & Time to Change One Tool (tc). With our tool, you need to enter the respective value for Machining and Operating Rate, Reference Cutting Velocity, Outside Radius of the Workpiece, Rotational Frequency of Spindle, Taylor's Tool Life Exponent, Workpiece Radius Ratio, Maximum Tool Life & 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.
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