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Machining and Operating Rate given Optimum Spindle Speed Formula

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Machining and Operating Rate spindle speed is the money charged for processing on and operating machines per unit time, including overheads. Check FAQs

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

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

Machining and Operating Rate given Optimum Spindle Speed Example

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Here is how the Machining and Operating Rate given Optimum Spindle Speed equation looks like with Values.

Here is how the Machining and Operating Rate given Optimum Spindle Speed equation looks like with Units.

Here is how the Machining and Operating Rate given Optimum Spindle Speed equation looks like.

114093.0388 = (\frac{158.8131}{{(\frac{5000}{2 \cdot 3.1416 \cdot 1000 \cdot 600})}^{\frac{1}{0.5129}} \cdot (\frac{1 + 0.5129}{1 - 0.5129}) \cdot (\frac{1 - 0.45}{1 - {0.45}^{\frac{0.5129 + 1}{0.5129}}}) \cdot 5} - 0.6)

114093.0388 = (\frac{158.8131}{{(\frac{5000mm/min}{2 \cdot 3.1416 \cdot 1000mm \cdot 600rev/min})}^{\frac{1}{0.5129}} \cdot (\frac{1 + 0.5129}{1 - 0.5129}) \cdot (\frac{1 - 0.45}{1 - {0.45}^{\frac{0.5129 + 1}{0.5129}}}) \cdot 5min} - 0.6min)

114093.0388 = (\frac{158.8131}{{(\frac{5000}{2 \cdot 3.1416 \cdot 1000 \cdot 600})}^{\frac{1}{0.5129}} \cdot (\frac{1 + 0.5129}{1 - 0.5129}) \cdot (\frac{1 - 0.45}{1 - {0.45}^{\frac{0.5129 + 1}{0.5129}}}) \cdot 5} - 0.6)

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Machining and Operating Rate given Optimum Spindle Speed Solution

Follow our step by step solution on how to calculate Machining and Operating Rate given Optimum Spindle Speed?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

M s = (\frac{158.8131}{{(\frac{5000mm/min}{2 \cdot π \cdot 1000mm \cdot 600rev/min})}^{\frac{1}{0.5129}} \cdot (\frac{1 + 0.5129}{1 - 0.5129}) \cdot (\frac{1 - 0.45}{1 - {0.45}^{\frac{0.5129 + 1}{0.5129}}}) \cdot 5min} - 0.6min)

Next Step Substitute values of Constants

∴

M s = (\frac{158.8131}{{(\frac{5000mm/min}{2 \cdot 3.1416 \cdot 1000mm \cdot 600rev/min})}^{\frac{1}{0.5129}} \cdot (\frac{1 + 0.5129}{1 - 0.5129}) \cdot (\frac{1 - 0.45}{1 - {0.45}^{\frac{0.5129 + 1}{0.5129}}}) \cdot 5min} - 0.6min)

Next Step Convert Units

∴

M s = (\frac{158.8131}{{(\frac{0.0833m/s}{2 \cdot 3.1416 \cdot 1m \cdot 10Hz})}^{\frac{1}{0.5129}} \cdot (\frac{1 + 0.5129}{1 - 0.5129}) \cdot (\frac{1 - 0.45}{1 - {0.45}^{\frac{0.5129 + 1}{0.5129}}}) \cdot 300s} - 36s)

Next Step Prepare to Evaluate

∴

M s = (\frac{158.8131}{{(\frac{0.0833}{2 \cdot 3.1416 \cdot 1 \cdot 10})}^{\frac{1}{0.5129}} \cdot (\frac{1 + 0.5129}{1 - 0.5129}) \cdot (\frac{1 - 0.45}{1 - {0.45}^{\frac{0.5129 + 1}{0.5129}}}) \cdot 300} - 36)

Next Step Evaluate

∴

M s = 114093.038842921

LAST Step Rounding Answer

∴

M s = 114093.0388

Machining and Operating Rate given Optimum Spindle Speed Formula Elements

Variables

Constants

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.

Symbol: M_s

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Machining and Operating Rate Spindle Speed

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 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

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

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

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

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

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 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 Machining and Operating Rate given Optimum Spindle Speed?

Machining and Operating Rate given Optimum Spindle Speed evaluator 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 evaluate 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_s symbol.

How to evaluate Machining and Operating Rate given Optimum Spindle Speed using this online evaluator? To use this online evaluator 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 (ω_s), Taylor's Tool Life Exponent (n), Workpiece Radius Ratio (R_w), Reference Tool Life (T_ref) & Time to Change One Tool (t_c) and hit the calculate button.

FAQs on Machining and Operating Rate given Optimum Spindle Speed

What is the formula to find Machining and Operating Rate given Optimum Spindle Speed?

The formula of Machining and Operating Rate given Optimum Spindle Speed is expressed as 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). Here is an example- 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).

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

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

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Machining and Operating Rate given Optimum Spindle Speed Formula

Machining and Operating Rate given Optimum Spindle Speed Example

Machining and Operating Rate given Optimum Spindle Speed Solution

Machining and Operating Rate given Optimum Spindle Speed Formula Elements

Other formulas in Cutting Speed category

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

FAQs on Machining and Operating Rate given Optimum Spindle Speed

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