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Cost of 1 Tool given Optimum Spindle Speed Formula

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The Cost of a Tool refers to the expenses associated with acquiring and using cutting tools used in various machining operations. Check FAQs

C t = (M \cdot {(\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 max) - t c

C_t - Cost of a Tool?M - Machining and Operating Rate?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_max - Maximum Tool Life?t_c - Time to Change One Tool?π - Archimedes' constant?

Cost of 1 Tool given Optimum Spindle Speed Example

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Here is how the Cost of 1 Tool given Optimum Spindle Speed equation looks like with Values.

Here is how the Cost of 1 Tool given Optimum Spindle Speed equation looks like with Units.

Here is how the Cost of 1 Tool given Optimum Spindle Speed equation looks like.

158.8131 = (100 \cdot {(\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 7000) - 0.6

158.8131 = (100 \cdot {(\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 7000min) - 0.6min

158.8131 = (100 \cdot {(\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 7000) - 0.6

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Cost of 1 Tool given Optimum Spindle Speed Solution

Follow our step by step solution on how to calculate Cost of 1 Tool given Optimum Spindle Speed?

FIRST Step Consider the formula

C t = (M \cdot {(\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 max) - t c

Next Step Substitute values of Variables

∴

C t = (100 \cdot {(\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 7000min) - 0.6min

Next Step Substitute values of Constants

∴

C t = (100 \cdot {(\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 7000min) - 0.6min

Next Step Convert Units

∴

C t = (100 \cdot {(\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 420000s) - 36s

Next Step Prepare to Evaluate

∴

C t = (100 \cdot {(\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 420000) - 36

Next Step Evaluate

∴

C t = 158.813118776906

LAST Step Rounding Answer

∴

C t = 158.8131

Cost of 1 Tool given Optimum Spindle Speed Formula Elements

Variables

Constants

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

Machining and Operating Rate

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

Symbol: M

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Machining and Operating Rate

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

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

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 Cost of 1 Tool given Optimum Spindle Speed?

Cost of 1 Tool given Optimum Spindle Speed evaluator uses 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 to evaluate the Cost of a Tool, The Cost of 1 Tool given Optimum Spindle Speed is a method to determine the maximum amount available to be spent on renewing the Machining Tool, such that the Production Cost is Minimum. The cost of one tool in metal machining can be calculated based on various factors, including the cost of the cutting tool itself, the machining parameters, and the production volume. The optimum spindle speed is one of the parameters that influences tool life and, subsequently, the cost of one tool. Cost of a Tool is denoted by C_t symbol.

How to evaluate Cost of 1 Tool given Optimum Spindle Speed using this online evaluator? To use this online evaluator for Cost of 1 Tool given Optimum Spindle Speed, enter Machining and Operating Rate (M), 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), Maximum Tool Life (T_max) & Time to Change One Tool (t_c) and hit the calculate button.

FAQs on Cost of 1 Tool given Optimum Spindle Speed

What is the formula to find Cost of 1 Tool given Optimum Spindle Speed?

The formula of Cost of 1 Tool given Optimum Spindle Speed is expressed as 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. Here is an example- 158.8131 = (100*(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)))*420000)-36.

How to calculate Cost of 1 Tool given Optimum Spindle Speed?

With Machining and Operating Rate (M), 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), Maximum Tool Life (T_max) & Time to Change One Tool (t_c) we can find Cost of 1 Tool given Optimum Spindle Speed using the formula - 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. This formula also uses Archimedes' constant .

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Cost of 1 Tool given Optimum Spindle Speed Formula

Cost of 1 Tool given Optimum Spindle Speed Example

Cost of 1 Tool given Optimum Spindle Speed Solution

Cost of 1 Tool given Optimum Spindle Speed Formula Elements

Other formulas in Cutting Speed category

How to Evaluate Cost of 1 Tool given Optimum Spindle Speed?

FAQs on Cost of 1 Tool given Optimum Spindle Speed

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