Reference Cutting Velocity given Optimum Spindle Speed Calculator

✖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%
✖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%
✖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%
✖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%
✖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%

✖Reference Cutting Velocity Spindle Speed 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 given Optimum Spindle Speed [V_ss]

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Reference Cutting Velocity given Optimum Spindle Speed

Formula

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

Example

`"930230.1mm/min"="600rev/min"*2*pi*"1000mm"*(((1-"0.512942")*("158.8131"*"0.6min"+"158.8131")*(1-("0.45")^((1+"0.512942")/"0.512942")))/((1+"0.512942")*"158.8131"*"5min"*(1-"0.45")))^"0.512942"`

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Reference Cutting Velocity given Optimum Spindle Speed Solution

STEP 0: Pre-Calculation Summary

Formula Used

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
V_ss = n_s*2*pi*R_o*(((1-n)*(C_t*t_c+C_t)*(1-a_r^((1+n)/n)))/((1+n)*C_t*T_ref*(1-a_r)))^n
This formula uses 1 Constants, 8 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Reference Cutting Velocity Spindle Speed - (Measured in Meter per Second) - Reference Cutting Velocity Spindle Speed refers to a standard cutting speed used as a baseline or reference point for selecting appropriate cutting speeds for specific machining operations.
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.
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.
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.
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.
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.

STEP 1: Convert Input(s) to Base Unit

Rotational Frequency of Spindle: 600 Revolution per Minute --> 10 Hertz (Check conversion here)
Outer Radius of Workpiece: 1000 Millimeter --> 1 Meter (Check conversion here)
Taylor's Tool Life Exponent: 0.512942 --> No Conversion Required
Cost of a Tool: 158.8131 --> No Conversion Required
Time to Change One Tool: 0.6 Minute --> 36 Second (Check conversion here)
Workpiece Radius Ratio: 0.45 --> No Conversion Required
Reference Tool Life: 5 Minute --> 300 Second (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

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

Evaluating ... ...

V_ss = 15.5038354846478

STEP 3: Convert Result to Output's Unit

15.5038354846478 Meter per Second -->930230.129078866 Millimeter per Minute (Check conversion here)

FINAL ANSWER

930230.129078866 ≈ 930230.1 Millimeter per Minute <-- Reference Cutting Velocity Spindle Speed

(Calculation completed in 00.004 seconds)

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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

Reference Cutting Velocity given Optimum Spindle Speed Formula

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 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 to calculate the Reference Cutting Velocity Spindle Speed, The Reference Cutting Velocity given Optimum Spindle Speed refers to the desired linear velocity at a specific point on the cutting edge of the tool as it engages with the workpiece during machining. This reference velocity is chosen based on factors such as material properties, tooling, and machining conditions, and it serves as a target for achieving optimal machining performance. Reference Cutting Velocity Spindle Speed is denoted by V_ss 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 (n_s), Outer Radius of Workpiece (R_o), Taylor's Tool Life Exponent (n), Cost of a Tool (C_t), Time to Change One Tool (t_c), Workpiece Radius Ratio (a_r) & Reference Tool Life (T_ref) and hit the calculate button. Here is how the Reference Cutting Velocity given Optimum Spindle Speed calculation can be explained with given input values -> 5.6E+10 = 10*2*pi*1*(((1-0.512942)*(158.8131*36+158.8131)*(1-0.45^((1+0.512942)/0.512942)))/((1+0.512942)*158.8131*300*(1-0.45)))^0.512942.

FAQ

What is Reference Cutting Velocity given Optimum Spindle Speed?

The Reference Cutting Velocity given Optimum Spindle Speed refers to the desired linear velocity at a specific point on the cutting edge of the tool as it engages with the workpiece during machining. This reference velocity is chosen based on factors such as material properties, tooling, and machining conditions, and it serves as a target for achieving optimal machining performance and is represented as V_ss = n_s*2*pi*R_o*(((1-n)*(C_t*t_c+C_t)*(1-a_r^((1+n)/n)))/((1+n)*C_t*T_ref*(1-a_r)))^n or 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. 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, 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, The Cost of a Tool refers to the expenses associated with acquiring and using cutting tools used in various machining operations, Time to Change One Tool refers to the duration required to replace a cutting tool with another tool during a machining operation, 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.

How to calculate Reference Cutting Velocity given Optimum Spindle Speed?

The Reference Cutting Velocity given Optimum Spindle Speed refers to the desired linear velocity at a specific point on the cutting edge of the tool as it engages with the workpiece during machining. This reference velocity is chosen based on factors such as material properties, tooling, and machining conditions, and it serves as a target for achieving optimal machining performance is calculated using 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. To calculate Reference Cutting Velocity given Optimum Spindle Speed, you need Rotational Frequency of Spindle (n_s), Outer Radius of Workpiece (R_o), Taylor's Tool Life Exponent (n), Cost of a Tool (C_t), Time to Change One Tool (t_c), Workpiece Radius Ratio (a_r) & Reference Tool Life (T_ref). With our tool, you need to enter the respective value for Rotational Frequency of Spindle, Outer Radius of Workpiece, Taylor's Tool Life Exponent, Cost of a Tool, Time to Change One Tool, Workpiece Radius Ratio & Reference Tool Life 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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