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Optimum Spindle Speed given Tool Changing Cost Formula

GoOptimum Spindle Speed 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 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}

ω_s - Rotational Frequency of Spindle?V_ref - Reference Cutting Velocity?R_o - Outer Radius of Workpiece?n - Taylor's Tool Life Exponent?C_t - Cost of a Tool?T_max - Maximum Tool Life?R_w - Workpiece Radius Ratio?C_ct - Cost of Changing Each Tool?π - Archimedes' constant?

Optimum Spindle Speed given Tool Changing Cost Example

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Here is how the Optimum Spindle Speed given Tool Changing Cost equation looks like with Values.

Here is how the Optimum Spindle Speed given Tool Changing Cost equation looks like with Units.

Here is how the Optimum Spindle Speed given Tool Changing Cost equation looks like.

600 = (\frac{5000}{2 \cdot 3.1416 \cdot 1000}) \cdot {(\frac{(1 + 0.5129) \cdot 158.8131 \cdot 7000 \cdot (1 - 0.45)}{(1 - 0.5129) \cdot (150.5757 + 158.8131) \cdot (1 - {0.45}^{\frac{1 + 0.5129}{0.5129}})})}^{0.5129}

600rev/min = (\frac{5000mm/min}{2 \cdot 3.1416 \cdot 1000mm}) \cdot {(\frac{(1 + 0.5129) \cdot 158.8131 \cdot 7000min \cdot (1 - 0.45)}{(1 - 0.5129) \cdot (150.5757 + 158.8131) \cdot (1 - {0.45}^{\frac{1 + 0.5129}{0.5129}})})}^{0.5129}

600 = (\frac{5000}{2 \cdot 3.1416 \cdot 1000}) \cdot {(\frac{(1 + 0.5129) \cdot 158.8131 \cdot 7000 \cdot (1 - 0.45)}{(1 - 0.5129) \cdot (150.5757 + 158.8131) \cdot (1 - {0.45}^{\frac{1 + 0.5129}{0.5129}})})}^{0.5129}

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Optimum Spindle Speed given Tool Changing Cost Solution

Follow our step by step solution on how to calculate Optimum Spindle Speed given Tool Changing Cost?

FIRST Step Consider the formula

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}

Next Step Substitute values of Variables

∴

ω s = (\frac{5000mm/min}{2 \cdot π \cdot 1000mm}) \cdot {(\frac{(1 + 0.5129) \cdot 158.8131 \cdot 7000min \cdot (1 - 0.45)}{(1 - 0.5129) \cdot (150.5757 + 158.8131) \cdot (1 - {0.45}^{\frac{1 + 0.5129}{0.5129}})})}^{0.5129}

Next Step Substitute values of Constants

∴

ω s = (\frac{5000mm/min}{2 \cdot 3.1416 \cdot 1000mm}) \cdot {(\frac{(1 + 0.5129) \cdot 158.8131 \cdot 7000min \cdot (1 - 0.45)}{(1 - 0.5129) \cdot (150.5757 + 158.8131) \cdot (1 - {0.45}^{\frac{1 + 0.5129}{0.5129}})})}^{0.5129}

Next Step Convert Units

∴

ω s = (\frac{0.0833m/s}{2 \cdot 3.1416 \cdot 1m}) \cdot {(\frac{(1 + 0.5129) \cdot 158.8131 \cdot 420000s \cdot (1 - 0.45)}{(1 - 0.5129) \cdot (150.5757 + 158.8131) \cdot (1 - {0.45}^{\frac{1 + 0.5129}{0.5129}})})}^{0.5129}

Next Step Prepare to Evaluate

∴

ω s = (\frac{0.0833}{2 \cdot 3.1416 \cdot 1}) \cdot {(\frac{(1 + 0.5129) \cdot 158.8131 \cdot 420000 \cdot (1 - 0.45)}{(1 - 0.5129) \cdot (150.5757 + 158.8131) \cdot (1 - {0.45}^{\frac{1 + 0.5129}{0.5129}})})}^{0.5129}

Next Step Evaluate

∴

ω s = 9.99999922303691Hz

Next Step Convert to Output's Unit

∴

ω s = 599.999953382214rev/min

LAST Step Rounding Answer

∴

ω s = 600rev/min

Optimum Spindle Speed given Tool Changing Cost 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

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.

Symbol: V_ref

Measurement: SpeedUnit: mm/min

Note: Value should be greater than 0.

Formulas to find Reference Cutting Velocity

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

Maximum Tool Life

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.

Symbol: T_max

Measurement: TimeUnit: min

Note: Value should be greater than 0.

Formulas to find Maximum 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

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.

Symbol: C_ct

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Cost of Changing Each 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

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}

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 given Tool Changing Cost?

Optimum Spindle Speed given Tool Changing Cost evaluator uses 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 to evaluate the Rotational Frequency of Spindle, The Optimum Spindle Speed given Tool Changing Cost 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 given Tool Changing Cost using this online evaluator? To use this online evaluator for Optimum Spindle Speed given Tool Changing Cost, enter Reference Cutting Velocity (V_ref), Outer Radius of Workpiece (R_o), Taylor's Tool Life Exponent (n), Cost of a Tool (C_t), Maximum Tool Life (T_max), Workpiece Radius Ratio (R_w) & Cost of Changing Each Tool (C_ct) and hit the calculate button.

FAQs on Optimum Spindle Speed given Tool Changing Cost

What is the formula to find Optimum Spindle Speed given Tool Changing Cost?

The formula of Optimum Spindle Speed given Tool Changing Cost is expressed as 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. Here is an example- 36000 = (0.0833333333333333/(2*pi*1))*(((1+0.512942)*158.8131*420000*(1-0.45))/((1-0.512942)*(150.5757+158.8131)*(1-0.45^((1+0.512942)/0.512942))))^0.512942.

How to calculate Optimum Spindle Speed given Tool Changing Cost?

With Reference Cutting Velocity (V_ref), Outer Radius of Workpiece (R_o), Taylor's Tool Life Exponent (n), Cost of a Tool (C_t), Maximum Tool Life (T_max), Workpiece Radius Ratio (R_w) & Cost of Changing Each Tool (C_ct) we can find Optimum Spindle Speed given Tool Changing Cost using the formula - 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. 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 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
Rotational Frequency of Spindle=Cutting Velocity/(2*pi*Instantaneous Radius for Cut)

Can the Optimum Spindle Speed given Tool Changing Cost be negative?

No, the Optimum Spindle Speed given Tool Changing Cost, measured in Frequency cannot be negative.

Which unit is used to measure Optimum Spindle Speed given Tool Changing Cost?

Optimum Spindle Speed given Tool Changing Cost 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 given Tool Changing Cost can be measured.

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Optimum Spindle Speed given Tool Changing Cost Formula

​GoOptimum Spindle Speed Formula

​GoRotational Frequency of Spindle given Cutting Speed Formula

Optimum Spindle Speed given Tool Changing Cost Example

Optimum Spindle Speed given Tool Changing Cost Solution

Optimum Spindle Speed given Tool Changing Cost Formula Elements

Other Formulas to find Rotational Frequency of Spindle

Other formulas in Cutting Speed category

How to Evaluate Optimum Spindle Speed given Tool Changing Cost?

FAQs on Optimum Spindle Speed given Tool Changing Cost

Variable Name

GoOptimum Spindle Speed Formula

GoRotational Frequency of Spindle given Cutting Speed Formula