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Reference Cutting Velocity given Optimum Spindle Speed Formula

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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. Check FAQs

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

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

Reference Cutting Velocity given Optimum Spindle Speed Example

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Here is how the Reference Cutting Velocity given Optimum Spindle Speed equation looks like with Values.

Here is how the Reference Cutting Velocity given Optimum Spindle Speed equation looks like with Units.

Here is how the Reference Cutting Velocity given Optimum Spindle Speed equation looks like.

930230.1291 = 600 \cdot 2 \cdot 3.1416 \cdot 1000 \cdot {(\frac{(1 - 0.5129) \cdot (158.8131 \cdot 0.6 + 158.8131) \cdot (1 - {0.45}^{\frac{1 + 0.5129}{0.5129}})}{(1 + 0.5129) \cdot 158.8131 \cdot 5 \cdot (1 - 0.45)})}^{0.5129}

930230.1291mm/min = 600rev/min \cdot 2 \cdot 3.1416 \cdot 1000mm \cdot {(\frac{(1 - 0.5129) \cdot (158.8131 \cdot 0.6min + 158.8131) \cdot (1 - {0.45}^{\frac{1 + 0.5129}{0.5129}})}{(1 + 0.5129) \cdot 158.8131 \cdot 5min \cdot (1 - 0.45)})}^{0.5129}

930230.1291 = 600 \cdot 2 \cdot 3.1416 \cdot 1000 \cdot {(\frac{(1 - 0.5129) \cdot (158.8131 \cdot 0.6 + 158.8131) \cdot (1 - {0.45}^{\frac{1 + 0.5129}{0.5129}})}{(1 + 0.5129) \cdot 158.8131 \cdot 5 \cdot (1 - 0.45)})}^{0.5129}

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Reference Cutting Velocity given Optimum Spindle Speed Solution

Follow our step by step solution on how to calculate Reference Cutting Velocity given Optimum Spindle Speed?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

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

Next Step Substitute values of Constants

∴

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

Next Step Convert Units

∴

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

Next Step Prepare to Evaluate

∴

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

Next Step Evaluate

∴

V s = 15.5038354846478m/s

Next Step Convert to Output's Unit

∴

V s = 930230.129078866mm/min

LAST Step Rounding Answer

∴

V s = 930230.1291mm/min

Reference Cutting Velocity given Optimum Spindle Speed Formula Elements

Variables

Constants

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

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

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

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

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

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 Reference Cutting Velocity given Optimum Spindle Speed?

Reference Cutting Velocity given Optimum Spindle Speed evaluator 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 evaluate 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_s symbol.

How to evaluate Reference Cutting Velocity given Optimum Spindle Speed using this online evaluator? To use this online evaluator for Reference Cutting Velocity given Optimum Spindle Speed, enter Rotational Frequency of Spindle (ω_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 (R_w) & Reference Tool Life (T_ref) and hit the calculate button.

FAQs on Reference Cutting Velocity given Optimum Spindle Speed

What is the formula to find Reference Cutting Velocity given Optimum Spindle Speed?

The formula of Reference Cutting Velocity given Optimum Spindle Speed is expressed as 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. Here is an example- 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.

How to calculate Reference Cutting Velocity given Optimum Spindle Speed?

With Rotational Frequency of Spindle (ω_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 (R_w) & Reference Tool Life (T_ref) we can find Reference Cutting Velocity given Optimum Spindle Speed using the formula - 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. This formula also uses Archimedes' constant .

Can the Reference Cutting Velocity given Optimum Spindle Speed be negative?

No, the Reference Cutting Velocity given Optimum Spindle Speed, measured in Speed cannot be negative.

Which unit is used to measure Reference Cutting Velocity given Optimum Spindle Speed?

Reference Cutting Velocity given Optimum Spindle Speed is usually measured using the Millimeter per Minute[mm/min] for Speed. Meter per Second[mm/min], Meter per Minute[mm/min], Meter per Hour[mm/min] are the few other units in which Reference Cutting Velocity given Optimum Spindle Speed can be measured.

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Reference Cutting Velocity given Optimum Spindle Speed Formula

Reference Cutting Velocity given Optimum Spindle Speed Example

Reference Cutting Velocity given Optimum Spindle Speed Solution

Reference Cutting Velocity given Optimum Spindle Speed Formula Elements

Other formulas in Cutting Speed category

How to Evaluate Reference Cutting Velocity given Optimum Spindle Speed?

FAQs on Reference Cutting Velocity given Optimum Spindle Speed

Variable Name