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Optimum Spindle Speed Formula

GoOptimum Spindle Speed given Tool Changing Cost Formula

GoRotational Frequency of Spindle given Cutting Speed Formula

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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. Check FAQs

ω s = (\frac{V s}{2 \cdot π \cdot R o}) \cdot {(\frac{(1 + n) \cdot C t \cdot T ref \cdot (1 - R w)}{(1 - n) \cdot (C t \cdot t c + C t) \cdot (1 - {R w}^{\frac{1 + n}{n}})})}^{n}

ω_s - Rotational Frequency of Spindle?V_s - Reference Cutting Velocity Spindle Speed?R_o - Outer Radius of Workpiece?n - Taylor's Tool Life Exponent?C_t - Cost of a Tool?T_ref - Reference Tool Life?R_w - Workpiece Radius Ratio?t_c - Time to Change One Tool?π - Archimedes' constant?

Optimum Spindle Speed Example

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With units

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Here is how the Optimum Spindle Speed equation looks like with Values.

Here is how the Optimum Spindle Speed equation looks like with Units.

Here is how the Optimum Spindle Speed equation looks like.

600 = (\frac{930230.1}{2 \cdot 3.1416 \cdot 1000}) \cdot {(\frac{(1 + 0.5129) \cdot 158.8131 \cdot 5 \cdot (1 - 0.45)}{(1 - 0.5129) \cdot (158.8131 \cdot 0.6 + 158.8131) \cdot (1 - {0.45}^{\frac{1 + 0.5129}{0.5129}})})}^{0.5129}

600rev/min = (\frac{930230.1mm/min}{2 \cdot 3.1416 \cdot 1000mm}) \cdot {(\frac{(1 + 0.5129) \cdot 158.8131 \cdot 5min \cdot (1 - 0.45)}{(1 - 0.5129) \cdot (158.8131 \cdot 0.6min + 158.8131) \cdot (1 - {0.45}^{\frac{1 + 0.5129}{0.5129}})})}^{0.5129}

600 = (\frac{930230.1}{2 \cdot 3.1416 \cdot 1000}) \cdot {(\frac{(1 + 0.5129) \cdot 158.8131 \cdot 5 \cdot (1 - 0.45)}{(1 - 0.5129) \cdot (158.8131 \cdot 0.6 + 158.8131) \cdot (1 - {0.45}^{\frac{1 + 0.5129}{0.5129}})})}^{0.5129}

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Optimum Spindle Speed Solution

Follow our step by step solution on how to calculate Optimum Spindle Speed?

FIRST Step Consider the formula

ω s = (\frac{V s}{2 \cdot π \cdot R o}) \cdot {(\frac{(1 + n) \cdot C t \cdot T ref \cdot (1 - R w)}{(1 - n) \cdot (C t \cdot t c + C t) \cdot (1 - {R w}^{\frac{1 + n}{n}})})}^{n}

Next Step Substitute values of Variables

∴

ω s = (\frac{930230.1mm/min}{2 \cdot π \cdot 1000mm}) \cdot {(\frac{(1 + 0.5129) \cdot 158.8131 \cdot 5min \cdot (1 - 0.45)}{(1 - 0.5129) \cdot (158.8131 \cdot 0.6min + 158.8131) \cdot (1 - {0.45}^{\frac{1 + 0.5129}{0.5129}})})}^{0.5129}

Next Step Substitute values of Constants

∴

ω s = (\frac{930230.1mm/min}{2 \cdot 3.1416 \cdot 1000mm}) \cdot {(\frac{(1 + 0.5129) \cdot 158.8131 \cdot 5min \cdot (1 - 0.45)}{(1 - 0.5129) \cdot (158.8131 \cdot 0.6min + 158.8131) \cdot (1 - {0.45}^{\frac{1 + 0.5129}{0.5129}})})}^{0.5129}

Next Step Convert Units

∴

ω s = (\frac{15.5038m/s}{2 \cdot 3.1416 \cdot 1m}) \cdot {(\frac{(1 + 0.5129) \cdot 158.8131 \cdot 300s \cdot (1 - 0.45)}{(1 - 0.5129) \cdot (158.8131 \cdot 36s + 158.8131) \cdot (1 - {0.45}^{\frac{1 + 0.5129}{0.5129}})})}^{0.5129}

Next Step Prepare to Evaluate

∴

ω s = (\frac{15.5038}{2 \cdot 3.1416 \cdot 1}) \cdot {(\frac{(1 + 0.5129) \cdot 158.8131 \cdot 300 \cdot (1 - 0.45)}{(1 - 0.5129) \cdot (158.8131 \cdot 36 + 158.8131) \cdot (1 - {0.45}^{\frac{1 + 0.5129}{0.5129}})})}^{0.5129}

Next Step Evaluate

∴

ω s = 9.99999968740138Hz

Next Step Convert to Output's Unit

∴

ω s = 599.999981244083rev/min

LAST Step Rounding Answer

∴

ω s = 600rev/min

Optimum Spindle Speed Formula Elements

Variables

Constants

Rotational Frequency of Spindle

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.

Symbol: ω_s

Measurement: FrequencyUnit: rev/min

Note: Value should be greater than 0.

Formulas to find Rotational Frequency of Spindle

Reference Cutting Velocity Spindle Speed

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.

Symbol: V_s

Measurement: SpeedUnit: mm/min

Note: Value should be greater than 0.

Formulas to find Reference Cutting Velocity Spindle Speed

Outer Radius of Workpiece

Outer Radius of Workpiece is the distance from the center of rotation to the outermost surface of the workpiece being machined.

Symbol: R_o

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Outer Radius of Workpiece

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.

Symbol: n

Measurement: NAUnit: Unitless

Note: Value should be between 0 to 1.

Formulas to find Taylor's Tool Life Exponent

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.

Symbol: C_t

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Cost of a Tool

Reference Tool Life

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.

Symbol: T_ref

Measurement: TimeUnit: min

Note: Value should be greater than 0.

Formulas to find Reference Tool Life

Workpiece Radius Ratio

Workpiece Radius Ratio refers to the ratio between the initial radius and the final radius of the workpiece being machined.

Symbol: R_w

Measurement: NAUnit: Unitless

Note: Value should be between 0 to 1.

Formulas to find Workpiece Radius Ratio

Time to Change One Tool

Time to Change One Tool refers to the duration required to replace a cutting tool with another tool during a machining operation.

Symbol: t_c

Measurement: TimeUnit: min

Note: Value should be greater than 0.

Formulas to find Time to Change One Tool

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

Other Formulas to find Rotational Frequency of Spindle

Go Optimum Spindle Speed given Tool Changing Cost

ω s = (\frac{V ref}{2 \cdot π \cdot R o}) \cdot {(\frac{(1 + n) \cdot C t \cdot T max \cdot (1 - R w)}{(1 - n) \cdot (C ct + C t) \cdot (1 - {R w}^{\frac{1 + n}{n}})})}^{n}

Go Rotational Frequency of Spindle given Cutting Speed

ω s = \frac{V}{2 \cdot π \cdot r}

Other formulas in Cutting Speed category

Go Reference Cutting Velocity given Rate of Increase of Wear-Land Width

V ref = \frac{V}{{(V r \cdot \frac{T ref}{w})}^{n}}

Go Cutting Velocity given Rate of Increase of Wear-Land Width

V = V ref \cdot {(V r \cdot \frac{T ref}{w})}^{n}

How to Evaluate Optimum Spindle Speed?

Optimum Spindle Speed evaluator uses 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 to evaluate the Rotational Frequency of Spindle, Optimum spindle speed is critical for achieving efficient metal machining processes. Machinists often rely on experience, empirical data, manufacturer recommendations, and machining simulations to determine the optimum spindle speed for specific machining applications. Continuous monitoring and adjustment of spindle speed throughout the machining process help maintain optimal cutting conditions and maximize machining performance. Rotational Frequency of Spindle is denoted by ω_s symbol.

How to evaluate Optimum Spindle Speed using this online evaluator? To use this online evaluator for Optimum Spindle Speed, enter Reference Cutting Velocity Spindle Speed (V_s), Outer Radius of Workpiece (R_o), Taylor's Tool Life Exponent (n), Cost of a Tool (C_t), Reference Tool Life (T_ref), Workpiece Radius Ratio (R_w) & Time to Change One Tool (t_c) and hit the calculate button.

FAQs on Optimum Spindle Speed

What is the formula to find Optimum Spindle Speed?

The formula of Optimum Spindle Speed is expressed as 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. Here is an example- 36000 = (15.503835/(2*pi*1))*(((1+0.512942)*158.8131*300*(1-0.45))/((1-0.512942)*(158.8131*36+158.8131)*(1-0.45^((1+0.512942)/0.512942))))^0.512942.

How to calculate Optimum Spindle Speed?

With Reference Cutting Velocity Spindle Speed (V_s), Outer Radius of Workpiece (R_o), Taylor's Tool Life Exponent (n), Cost of a Tool (C_t), Reference Tool Life (T_ref), Workpiece Radius Ratio (R_w) & Time to Change One Tool (t_c) we can find Optimum Spindle Speed using the formula - 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. This formula also uses Archimedes' constant .

What are the other ways to Calculate Rotational Frequency of Spindle?

Here are the different ways to Calculate Rotational Frequency of Spindle-

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

Can the Optimum Spindle Speed be negative?

No, the Optimum Spindle Speed, measured in Frequency cannot be negative.

Which unit is used to measure Optimum Spindle Speed?

Optimum Spindle Speed is usually measured using the Revolution per Minute[rev/min] for Frequency. Hertz[rev/min], Petahertz[rev/min], Terahertz[rev/min] are the few other units in which Optimum Spindle Speed can be measured.

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Optimum Spindle Speed Formula

​GoOptimum Spindle Speed given Tool Changing Cost Formula

​GoRotational Frequency of Spindle given Cutting Speed Formula

Optimum Spindle Speed Example

Optimum Spindle Speed Solution

Optimum Spindle Speed Formula Elements

Other Formulas to find Rotational Frequency of Spindle

Other formulas in Cutting Speed category

How to Evaluate Optimum Spindle Speed?

FAQs on Optimum Spindle Speed

Variable Name

GoOptimum Spindle Speed given Tool Changing Cost Formula

GoRotational Frequency of Spindle given Cutting Speed Formula