FormulaDen.com

Physics Chemistry Math Chemical Engineering Civil Electrical Electronics Electronics and Instrumentation Materials Science Mechanical Production Engineering Financial Health

Reference Tool Life given Optimum Spindle Speed Formula

GoReference Tool Life given Cutting Speed for Constant-Cutting-Speed Operation Formula

Fx Copy

LaTeX Copy

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. Check FAQs

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

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

Reference Tool Life given Optimum Spindle Speed Example

With values

With units

Only example

Here is how the Reference Tool Life given Optimum Spindle Speed equation looks like with Values.

Here is how the Reference Tool Life given Optimum Spindle Speed equation looks like with Units.

Here is how the Reference Tool Life given Optimum Spindle Speed equation looks like.

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

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

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

Tip: Use pencil ( Pencil

) icon above to edit Input Values and Units.

Calculate

Recalculate

Solution

Copy

Reset

You are here -

Home » Category

Engineering » Category

Production Engineering » Category

Metal Machining » fx Reference Tool Life given Optimum Spindle Speed

Reference Tool Life given Optimum Spindle Speed Solution

Follow our step by step solution on how to calculate Reference Tool Life given Optimum Spindle Speed?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

T ref = \frac{{(600rev/min \cdot 2 \cdot π \cdot \frac{1000mm}{930230.1mm/min})}^{\frac{1}{0.5129}} \cdot (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 (1 - 0.45)}

Next Step Substitute values of Constants

∴

T ref = \frac{{(600rev/min \cdot 2 \cdot 3.1416 \cdot \frac{1000mm}{930230.1mm/min})}^{\frac{1}{0.5129}} \cdot (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 (1 - 0.45)}

Next Step Convert Units

∴

T ref = \frac{{(10Hz \cdot 2 \cdot 3.1416 \cdot \frac{1m}{15.5038m/s})}^{\frac{1}{0.5129}} \cdot (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 (1 - 0.45)}

Next Step Prepare to Evaluate

∴

T ref = \frac{{(10 \cdot 2 \cdot 3.1416 \cdot \frac{1}{15.5038})}^{\frac{1}{0.5129}} \cdot (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 (1 - 0.45)}

Next Step Evaluate

∴

T ref = 300.000018282689s

Next Step Convert to Output's Unit

∴

T ref = 5.00000030471148min

LAST Step Rounding Answer

∴

T ref = 5min

Reference Tool Life given Optimum Spindle Speed Formula Elements

Variables

Constants

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

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

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

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

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 Reference Tool Life

Go Reference Tool Life given Cutting Speed for Constant-Cutting-Speed Operation

T ref = {(\frac{V}{V ref})}^{\frac{1}{n}} \cdot Q \cdot L

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 Tool Life given Optimum Spindle Speed?

Reference Tool Life given Optimum Spindle Speed evaluator uses Reference Tool Life = ((Rotational Frequency of Spindle*2*pi*Outer Radius of Workpiece/Reference Cutting Velocity Spindle Speed)^(1/Taylor's Tool Life Exponent)*(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*(1-Workpiece Radius Ratio)) to evaluate the Reference Tool Life, The Reference Tool Life given Optimum Spindle Speed refers to the estimated or desired lifespan of a cutting tool operating at the ideal rotational speed of the spindle, which maximizes machining efficiency, tool life, and surface finish quality. Reference Tool Life is denoted by T_ref symbol.

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

FAQs on Reference Tool Life given Optimum Spindle Speed

What is the formula to find Reference Tool Life given Optimum Spindle Speed?

The formula of Reference Tool Life given Optimum Spindle Speed is expressed as Reference Tool Life = ((Rotational Frequency of Spindle*2*pi*Outer Radius of Workpiece/Reference Cutting Velocity Spindle Speed)^(1/Taylor's Tool Life Exponent)*(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*(1-Workpiece Radius Ratio)). Here is an example- 0.083333 = ((10*2*pi*1/15.503835)^(1/0.512942)*(1-0.512942)*(158.8131*36+158.8131)*(1-0.45^((1+0.512942)/0.512942)))/((1+0.512942)*158.8131*(1-0.45)).

How to calculate Reference Tool Life given Optimum Spindle Speed?

With Rotational Frequency of Spindle (ω_s), Outer Radius of Workpiece (R_o), Reference Cutting Velocity Spindle Speed (V_s), Taylor's Tool Life Exponent (n), Cost of a Tool (C_t), Time to Change One Tool (t_c) & Workpiece Radius Ratio (R_w) we can find Reference Tool Life given Optimum Spindle Speed using the formula - Reference Tool Life = ((Rotational Frequency of Spindle*2*pi*Outer Radius of Workpiece/Reference Cutting Velocity Spindle Speed)^(1/Taylor's Tool Life Exponent)*(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*(1-Workpiece Radius Ratio)). This formula also uses Archimedes' constant .

What are the other ways to Calculate Reference Tool Life?

Here are the different ways to Calculate Reference Tool Life-

Reference Tool Life=(Cutting Velocity/Reference Cutting Velocity)^(1/Taylor's Tool Life Exponent)*Time Proportion of Cutting Edge*Tool Life

Can the Reference Tool Life given Optimum Spindle Speed be negative?

No, the Reference Tool Life given Optimum Spindle Speed, measured in Time cannot be negative.

Which unit is used to measure Reference Tool Life given Optimum Spindle Speed?

Reference Tool Life given Optimum Spindle Speed is usually measured using the Minute[min] for Time. Second[min], Millisecond[min], Microsecond[min] are the few other units in which Reference Tool Life given Optimum Spindle Speed can be measured.

Let Others Know

✖

Facebook

Twitter

Copied!

Reference Tool Life given Optimum Spindle Speed Formula

​GoReference Tool Life given Cutting Speed for Constant-Cutting-Speed Operation Formula

Reference Tool Life given Optimum Spindle Speed Example

Reference Tool Life given Optimum Spindle Speed Solution

Reference Tool Life given Optimum Spindle Speed Formula Elements

Other Formulas to find Reference Tool Life

Other formulas in Cutting Speed category

How to Evaluate Reference Tool Life given Optimum Spindle Speed?

FAQs on Reference Tool Life given Optimum Spindle Speed

Variable Name

GoReference Tool Life given Cutting Speed for Constant-Cutting-Speed Operation Formula