Machining and Operating Rate 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%
✖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%
✖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%
✖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%
✖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%
✖Reference Tool Life refers to a standard or predetermined lifespan used as a baseline for estimating the expected durability of cutting tools under specific machining conditions.ⓘ Reference Tool Life [T_ref]			+10% -10%
✖Time to Change One Tool refers to the duration required to replace a cutting tool with another tool during a machining operation.ⓘ Time to Change One Tool [t_c]			+10% -10%

✖Machining and Operating Rate spindle speed is the money charged for processing on and operating machines per unit time, including overheads.ⓘ Machining and Operating Rate given Optimum Spindle Speed [M_ss]

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Machining and Operating Rate given Optimum Spindle Speed

Formula

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

Example

`"114093"=("158.8131"/(("5000mm/min"/(2*pi*"1000mm"*"600rev/min"))^(1/"0.512942")*((1+"0.512942")/(1-"0.512942"))*((1-"0.45")/(1-("0.45")^(("0.512942"+1)/"0.512942")))*"5min")-"0.6min")`

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Machining and Operating Rate given Optimum Spindle Speed Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)
M_ss = (C_t/((V_ref/(2*pi*R_o*n_s))^(1/n)*((1+n)/(1-n))*((1-a_r)/(1-a_r^((n+1)/n)))*T_ref)-t_c)
This formula uses 1 Constants, 9 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Machining and Operating Rate Spindle Speed - Machining and Operating Rate spindle speed is the money charged for processing on and operating machines per unit time, including overheads.
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.
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.
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.
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.
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.
Reference Tool Life - (Measured in Second) - Reference Tool Life refers to a standard or predetermined lifespan used as a baseline for estimating the expected durability of cutting tools under specific machining conditions.
Time to Change One Tool - (Measured in Second) - Time to Change One Tool refers to the duration required to replace a cutting tool with another tool during a machining operation.

STEP 1: Convert Input(s) to Base Unit

Cost of a Tool: 158.8131 --> No Conversion Required
Reference Cutting Velocity: 5000 Millimeter per Minute --> 0.0833333333333333 Meter per Second (Check conversion here)
Outer Radius of Workpiece: 1000 Millimeter --> 1 Meter (Check conversion here)
Rotational Frequency of Spindle: 600 Revolution per Minute --> 10 Hertz (Check conversion here)
Taylor's Tool Life Exponent: 0.512942 --> No Conversion Required
Workpiece Radius Ratio: 0.45 --> No Conversion Required
Reference Tool Life: 5 Minute --> 300 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

M_ss = (C_t/((V_ref/(2*pi*R_o*n_s))^(1/n)*((1+n)/(1-n))*((1-a_r)/(1-a_r^((n+1)/n)))*T_ref)-t_c) --> (158.8131/((0.0833333333333333/(2*pi*1*10))^(1/0.512942)*((1+0.512942)/(1-0.512942))*((1-0.45)/(1-0.45^((0.512942+1)/0.512942)))*300)-36)

Evaluating ... ...

M_ss = 114093.038842921

STEP 3: Convert Result to Output's Unit

114093.038842921 --> No Conversion Required

FINAL ANSWER

114093.038842921 ≈ 114093 <-- Machining and Operating Rate Spindle Speed

(Calculation completed in 00.004 seconds)

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Home » Engineering » Production Engineering » Metal Machining » Facing Operation » Machine Tools and Operations » Cutting Speed » Machining and Operating Rate given Optimum Spindle Speed

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

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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

Machining and Operating Rate given Optimum Spindle Speed Formula

Machining Rate and Operating Rate

The machining rate and operating rate in metal machining, given the optimum spindle speed, can be calculated using various formulas depending on specific factors such as cutting parameters, tooling, material properties, and machining conditions. Overall, the formulas for calculating machining rate and operating rate provide valuable insights into the productivity and efficiency of metal machining operations, helping machinists and engineers optimize cutting parameters, select appropriate tooling, and improve overall manufacturing performance.

How to Calculate Machining and Operating Rate given Optimum Spindle Speed?

Machining and Operating Rate given Optimum Spindle Speed calculator uses 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) to calculate the Machining and Operating Rate Spindle Speed, The Machining and Operating Rate given Optimum Spindle Speed is a method to determine the maximum amount that can be spent on Machining and Operating when the resources to be used are strictly bounded for minimum production cost. Machining and Operating Rate Spindle Speed is denoted by M_ss symbol.

How to calculate Machining and Operating Rate given Optimum Spindle Speed using this online calculator? To use this online calculator for Machining and Operating Rate given Optimum Spindle Speed, enter Cost of a Tool (C_t), Reference Cutting Velocity (V_ref), Outer Radius of Workpiece (R_o), Rotational Frequency of Spindle (n_s), Taylor's Tool Life Exponent (n), Workpiece Radius Ratio (a_r), Reference Tool Life (T_ref) & Time to Change One Tool (t_c) and hit the calculate button. Here is how the Machining and Operating Rate given Optimum Spindle Speed calculation can be explained with given input values -> 114093 = (158.8131/((0.0833333333333333/(2*pi*1*10))^(1/0.512942)*((1+0.512942)/(1-0.512942))*((1-0.45)/(1-0.45^((0.512942+1)/0.512942)))*300)-36).

FAQ

What is Machining and Operating Rate given Optimum Spindle Speed?

The Machining and Operating Rate given Optimum Spindle Speed is a method to determine the maximum amount that can be spent on Machining and Operating when the resources to be used are strictly bounded for minimum production cost and is represented as M_ss = (C_t/((V_ref/(2*pi*R_o*n_s))^(1/n)*((1+n)/(1-n))*((1-a_r)/(1-a_r^((n+1)/n)))*T_ref)-t_c) or 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). The Cost of a Tool refers to the expenses associated with acquiring and using cutting tools used in various machining operations, 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, Outer Radius of Workpiece is the distance from the center of rotation to the outermost surface of the workpiece being machined, 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, 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, Reference Tool Life refers to a standard or predetermined lifespan used as a baseline for estimating the expected durability of cutting tools under specific machining conditions & Time to Change One Tool refers to the duration required to replace a cutting tool with another tool during a machining operation.

How to calculate Machining and Operating Rate given Optimum Spindle Speed?

The Machining and Operating Rate given Optimum Spindle Speed is a method to determine the maximum amount that can be spent on Machining and Operating when the resources to be used are strictly bounded for minimum production cost is calculated using 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). To calculate Machining and Operating Rate given Optimum Spindle Speed, you need Cost of a Tool (C_t), Reference Cutting Velocity (V_ref), Outer Radius of Workpiece (R_o), Rotational Frequency of Spindle (n_s), Taylor's Tool Life Exponent (n), Workpiece Radius Ratio (a_r), Reference Tool Life (T_ref) & Time to Change One Tool (t_c). With our tool, you need to enter the respective value for Cost of a Tool, Reference Cutting Velocity, Outer Radius of Workpiece, Rotational Frequency of Spindle, Taylor's Tool Life Exponent, Workpiece Radius Ratio, Reference 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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