Tool Changing Cost given Optimum Spindle Speed Calculator

✖The Cost of a Tool refers to the expenses associated with acquiring and using cutting tools used in various machining operations.ⓘ Cost of a Tool [C_t]			+10% -10%
✖Maximum Tool Life is the point at which a cutting tool reaches its limit in terms of usage before it becomes too worn, damaged, or otherwise unable to effectively perform its intended function.ⓘ Maximum Tool Life [T_max]			+10% -10%
✖Rotational Frequency of Spindle is the speed at which the spindle of a machine tool rotates during machining operations. It is typically measured in revolutions per minute.ⓘ Rotational Frequency of Spindle [n_s]			+10% -10%
✖Outer Radius of Workpiece is the distance from the center of rotation to the outermost surface of the workpiece being machined.ⓘ Outer Radius of Workpiece [R_o]			+10% -10%
✖Reference Cutting Velocity refers to a standard cutting speed used as a baseline or reference point for selecting appropriate cutting speeds for specific machining operations.ⓘ Reference Cutting Velocity [V_ref]			+10% -10%
✖Taylor's Tool Life Exponent is a parameter used in tool life equations to describe the relationship between cutting speed and tool life in metal machining.ⓘ Taylor's Tool Life Exponent [n]			+10% -10%
✖Workpiece Radius Ratio refers to the ratio between the initial radius and the final radius of the workpiece being machined.ⓘ Workpiece Radius Ratio [a_r]			+10% -10%

✖The cost of changing each Tool is the cost that arises due to the time taken by the operator to change one tool when he is paid by the hour.ⓘ Tool Changing Cost given Optimum Spindle Speed [C_CT]

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Tool Changing Cost given Optimum Spindle Speed

Formula

`"C"_{"CT"} = (("C"_{"t"}*"T"_{"max"})/(("n"_{"s"}*2*pi*"R"_{"o"}/"V"_{"ref"})^(1/"n")*(1-"a"_{"r"}^((1+"n")/"n"))*(1-"n")/((1+"n")*(1-"a"_{"r"}))))-"C"_{"t"}`

Example

`"150.5757"=(("158.8131"*"7000min")/(("600rev/min"*2*pi*"1000mm"/"5000mm/min")^(1/"0.512942")*(1-("0.45")^((1+"0.512942")/"0.512942"))*(1-"0.512942")/((1+"0.512942")*(1-"0.45"))))-"158.8131"`

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Tool Changing Cost given Optimum Spindle Speed Solution

STEP 0: Pre-Calculation Summary

Formula Used

Cost of Changing Each Tool = ((Cost of a Tool*Maximum 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
C_CT = ((C_t*T_max)/((n_s*2*pi*R_o/V_ref)^(1/n)*(1-a_r^((1+n)/n))*(1-n)/((1+n)*(1-a_r))))-C_t
This formula uses 1 Constants, 8 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Cost of Changing Each Tool - The cost of changing each Tool is the cost that arises due to the time taken by the operator to change one tool when he is paid by the hour.
Cost of a Tool - The Cost of a Tool refers to the expenses associated with acquiring and using cutting tools used in various machining operations.
Maximum Tool Life - (Measured in Second) - Maximum Tool Life is the point at which a cutting tool reaches its limit in terms of usage before it becomes too worn, damaged, or otherwise unable to effectively perform its intended function.
Rotational Frequency of Spindle - (Measured in Hertz) - Rotational Frequency of Spindle is the speed at which the spindle of a machine tool rotates during machining operations. It is typically measured in revolutions per minute.
Outer Radius of Workpiece - (Measured in Meter) - Outer Radius of Workpiece is the distance from the center of rotation to the outermost surface of the workpiece being machined.
Reference Cutting Velocity - (Measured in Meter per Second) - Reference Cutting Velocity refers to a standard cutting speed used as a baseline or reference point for selecting appropriate cutting speeds for specific machining operations.
Taylor's Tool Life Exponent - Taylor's Tool Life Exponent is a parameter used in tool life equations to describe the relationship between cutting speed and tool life in metal machining.
Workpiece Radius Ratio - Workpiece Radius Ratio refers to the ratio between the initial radius and the final radius of the workpiece being machined.

STEP 1: Convert Input(s) to Base Unit

Cost of a Tool: 158.8131 --> No Conversion Required
Maximum Tool Life: 7000 Minute --> 420000 Second (Check conversion here)
Rotational Frequency of Spindle: 600 Revolution per Minute --> 10 Hertz (Check conversion here)
Outer Radius of 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: 0.512942 --> No Conversion Required
Workpiece Radius Ratio: 0.45 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

C_CT = ((C_t*T_max)/((n_s*2*pi*R_o/V_ref)^(1/n)*(1-a_r^((1+n)/n))*(1-n)/((1+n)*(1-a_r))))-C_t --> ((158.8131*420000)/((10*2*pi*1/0.0833333333333333)^(1/0.512942)*(1-0.45^((1+0.512942)/0.512942))*(1-0.512942)/((1+0.512942)*(1-0.45))))-158.8131

Evaluating ... ...

C_CT = 150.575653136286

STEP 3: Convert Result to Output's Unit

150.575653136286 --> No Conversion Required

FINAL ANSWER

150.575653136286 ≈ 150.5757 <-- Cost of Changing Each Tool

(Calculation completed in 00.008 seconds)

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Home » Engineering » Production Engineering » Metal Machining » Facing Operation » Machine Tools and Operations » Cutting Speed » Tool Changing Cost given Optimum Spindle Speed

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Created by Kumar Siddhant

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

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National Institute of Technology (NIT), Srinagar

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< 21 Cutting Speed Calculators

Reference Tool Life given Optimum Spindle Speed

Go Reference Tool Life = ((Rotational Frequency of Spindle*2*pi*Outer Radius of Workpiece/Reference Cutting Velocity Spindle Speed)^(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))

Optimum Spindle Speed

Go Rotational Frequency of Spindle = (Reference Cutting Velocity Spindle Speed/(2*pi*Outer Radius of 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

Reference Cutting Velocity given Optimum Spindle Speed

Go Reference Cutting Velocity Spindle Speed = Rotational Frequency of Spindle*2*pi*Outer Radius of Workpiece*(((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*Reference Tool Life*(1-Workpiece Radius Ratio)))^Taylor's Tool Life Exponent

Machining and Operating Rate given Optimum Spindle Speed

Go Machining and Operating Rate Spindle Speed = (Cost of a Tool/((Reference Cutting Velocity/(2*pi*Outer Radius of 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)

Tool Changing Time given Optimum Spindle Speed

Go Time to Change One Tool = (Machining and Operating Rate*(Reference Cutting Velocity/(2*pi*Outer Radius of 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)-Cost of a Tool

Cost of 1 Tool given Optimum Spindle Speed

Go Cost of a Tool = (Machining and Operating Rate*(Reference Cutting Velocity/(2*pi*Outer Radius of 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

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*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

Optimum Spindle Speed given Tool Changing Cost

Go Rotational Frequency of Spindle = (Reference Cutting Velocity/(2*pi*Outer Radius of Workpiece))*(((1+Taylor's Tool Life Exponent)*Cost of a Tool*Maximum 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

Taylor's Exponent given Cutting Speed for Constant-Cutting-Speed Operation

Go Taylor's Tool Life Exponent = ln(Cutting Velocity/Reference Cutting Velocity)/ln(Reference Tool Life/(Tool Life*Time Proportion of Cutting Edge))

Time for Facing given Instantaneous Cutting Speed

Go Process Time = (Outer Radius of Workpiece-(Cutting Velocity/(2*pi*Rotational Frequency of Spindle)))/(Rotational Frequency of Spindle*Feed)

Feed given Instantaneous Cutting Speed

Go Feed = (Outer Radius of Workpiece-(Cutting Velocity/(2*pi*Rotational Frequency of Spindle)))/(Rotational Frequency of Spindle*Process Time)

Instantaneous Cutting Speed given Feed

Go Cutting Velocity = 2*pi*Rotational Frequency of Spindle*(Outer Radius of 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

Time Proportion of Edge given Cutting Speed for Constant-Cutting-Speed Operation

Go Time Proportion of Cutting Edge = Reference Tool Life*((Reference Cutting Velocity/Cutting Velocity)^(1/Taylor's Tool Life Exponent))/Tool Life

Tool Life given Cutting Speed for Constant-Cutting-Speed Operation

Go Tool Life = Reference Tool Life*((Reference Cutting Velocity/Cutting Velocity)^(1/Taylor's Tool Life Exponent))/Time Proportion of Cutting Edge

Reference Cutting Velocity given Cutting Velocity for Constant-Cutting-Speed Operation

Go Reference Cutting Velocity = Cutting Velocity/((Reference Tool Life/(Tool Life*Time Proportion of Cutting Edge))^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*Tool Life

Cutting Speed for Constant-Cutting-Speed Operation

Go Cutting Velocity = (Reference Tool Life/(Tool Life*Time Proportion of Cutting Edge))^Taylor's Tool Life Exponent*Reference Cutting Velocity

Rotational Frequency of Spindle given Cutting Speed

Go Rotational Frequency of Spindle = Cutting Velocity/(2*pi*Instantaneous Radius for Cut)

Instantaneous Cutting Speed

Go Cutting Velocity = 2*pi*Rotational Frequency of Spindle*Instantaneous Radius for Cut

Tool Changing Cost given Optimum Spindle Speed Formula

How is Tool-Changing Cost generated?

The tool-changing cost is generated on the processes that basically include changing or re-sharpening the tool. These do not result in any productivity or profit whatsoever. But as the time is consumed by the operator to perform these tasks, when paid by the hour, the operators cost plants this time too.

How to Calculate Tool Changing Cost given Optimum Spindle Speed?

Tool Changing Cost given Optimum Spindle Speed calculator uses Cost of Changing Each Tool = ((Cost of a Tool*Maximum 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 to calculate the Cost of Changing Each Tool, The Tool Changing Cost given Optimum Spindle Speed refers to the expenses associated with changing or replacing cutting tools during the machining process. These costs include direct expenses such as the purchase cost of the tools, labor costs associated with tool changeovers, and indirect costs such as machine downtime and lost productivity. The optimum spindle speed, on the other hand, refers to the ideal rotational speed of the spindle that maximizes machining efficiency, tool life, and surface finish quality for a given machining operation. Cost of Changing Each Tool is denoted by C_CT symbol.

How to calculate Tool Changing Cost given Optimum Spindle Speed using this online calculator? To use this online calculator for Tool Changing Cost given Optimum Spindle Speed, enter Cost of a Tool (C_t), Maximum Tool Life (T_max), Rotational Frequency of Spindle (n_s), Outer Radius of Workpiece (R_o), Reference Cutting Velocity (V_ref), Taylor's Tool Life Exponent (n) & Workpiece Radius Ratio (a_r) and hit the calculate button. Here is how the Tool Changing Cost given Optimum Spindle Speed calculation can be explained with given input values -> 150.5757 = ((158.8131*420000)/((10*2*pi*1/0.0833333333333333)^(1/0.512942)*(1-0.45^((1+0.512942)/0.512942))*(1-0.512942)/((1+0.512942)*(1-0.45))))-158.8131.

FAQ

What is Tool Changing Cost given Optimum Spindle Speed?

The Tool Changing Cost given Optimum Spindle Speed refers to the expenses associated with changing or replacing cutting tools during the machining process. These costs include direct expenses such as the purchase cost of the tools, labor costs associated with tool changeovers, and indirect costs such as machine downtime and lost productivity. The optimum spindle speed, on the other hand, refers to the ideal rotational speed of the spindle that maximizes machining efficiency, tool life, and surface finish quality for a given machining operation and is represented as C_CT = ((C_t*T_max)/((n_s*2*pi*R_o/V_ref)^(1/n)*(1-a_r^((1+n)/n))*(1-n)/((1+n)*(1-a_r))))-C_t or Cost of Changing Each Tool = ((Cost of a Tool*Maximum 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. The Cost of a Tool refers to the expenses associated with acquiring and using cutting tools used in various machining operations, Maximum Tool Life is the point at which a cutting tool reaches its limit in terms of usage before it becomes too worn, damaged, or otherwise unable to effectively perform its intended function, Rotational Frequency of Spindle is the speed at which the spindle of a machine tool rotates during machining operations. It is typically measured in revolutions per minute, Outer Radius of Workpiece is the distance from the center of rotation to the outermost surface of the workpiece being machined, Reference Cutting Velocity refers to a standard cutting speed used as a baseline or reference point for selecting appropriate cutting speeds for specific machining operations, Taylor's Tool Life Exponent is a parameter used in tool life equations to describe the relationship between cutting speed and tool life in metal machining & Workpiece Radius Ratio refers to the ratio between the initial radius and the final radius of the workpiece being machined.

How to calculate Tool Changing Cost given Optimum Spindle Speed?

The Tool Changing Cost given Optimum Spindle Speed refers to the expenses associated with changing or replacing cutting tools during the machining process. These costs include direct expenses such as the purchase cost of the tools, labor costs associated with tool changeovers, and indirect costs such as machine downtime and lost productivity. The optimum spindle speed, on the other hand, refers to the ideal rotational speed of the spindle that maximizes machining efficiency, tool life, and surface finish quality for a given machining operation is calculated using Cost of Changing Each Tool = ((Cost of a Tool*Maximum 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. To calculate Tool Changing Cost given Optimum Spindle Speed, you need Cost of a Tool (C_t), Maximum Tool Life (T_max), Rotational Frequency of Spindle (n_s), Outer Radius of Workpiece (R_o), Reference Cutting Velocity (V_ref), Taylor's Tool Life Exponent (n) & Workpiece Radius Ratio (a_r). With our tool, you need to enter the respective value for Cost of a Tool, Maximum Tool Life, Rotational Frequency of Spindle, Outer Radius of Workpiece, Reference Cutting Velocity, Taylor's Tool Life Exponent & Workpiece Radius Ratio 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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