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Taylor's Exponent of Depth of Cut Formula

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Taylor's Exponent for Depth of Cut is an experimental exponent used to draw a relation between the depth of cut to workpiece and tool life. Check FAQs

b = \frac{\ln (\frac{C}{V \cdot (f^{a}) \cdot ({L max}^{y})})}{\ln (d)}

b - Taylor's Exponent for Depth of Cut?C - Taylor's Constant?V - Cutting Velocity?f - Feed Rate?a - Taylor's Exponent for Feed Rate in Taylors Theory?L_max - Maximum Tool Life?y - Taylor Tool Life Exponent?d - Depth of Cut?

Taylor's Exponent of Depth of Cut Example

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Here is how the Taylor's Exponent of Depth of Cut equation looks like with Values.

Here is how the Taylor's Exponent of Depth of Cut equation looks like with Units.

Here is how the Taylor's Exponent of Depth of Cut equation looks like.

0.24 = \frac{\ln (\frac{85.1306}{0.8333 \cdot ({0.7}^{0.2}) \cdot (4500^{0.8466})})}{\ln (0.013)}

0.24 = \frac{\ln (\frac{85.1306}{0.8333m/s \cdot ({0.7mm/rev}^{0.2}) \cdot ({4500s}^{0.8466})})}{\ln (0.013m)}

0.24 = \frac{\ln (\frac{85.1306}{0.8333 \cdot ({0.7}^{0.2}) \cdot (4500^{0.8466})})}{\ln (0.013)}

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Taylor's Exponent of Depth of Cut Solution

Follow our step by step solution on how to calculate Taylor's Exponent of Depth of Cut?

FIRST Step Consider the formula

b = \frac{\ln (\frac{C}{V \cdot (f^{a}) \cdot ({L max}^{y})})}{\ln (d)}

Next Step Substitute values of Variables

∴

b = \frac{\ln (\frac{85.1306}{0.8333m/s \cdot ({0.7mm/rev}^{0.2}) \cdot ({4500s}^{0.8466})})}{\ln (0.013m)}

Next Step Convert Units

∴

b = \frac{\ln (\frac{85.1306}{0.8333m/s \cdot ({0.0007m/rev}^{0.2}) \cdot ({4500s}^{0.8466})})}{\ln (0.013m)}

Next Step Prepare to Evaluate

∴

b = \frac{\ln (\frac{85.1306}{0.8333 \cdot ({0.0007}^{0.2}) \cdot (4500^{0.8466})})}{\ln (0.013)}

Next Step Evaluate

∴

b = 0.239998834629592

LAST Step Rounding Answer

∴

b = 0.24

Taylor's Exponent of Depth of Cut Formula Elements

Variables

Functions

Taylor's Exponent for Depth of Cut

Taylor's Exponent for Depth of Cut is an experimental exponent used to draw a relation between the depth of cut to workpiece and tool life.

Symbol: b

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Taylor's Exponent for Depth of Cut

Taylor's Constant

Taylor's Constant is an experimental constant that depends mainly upon the tool-work materials and the cutting environment.

Symbol: C

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Taylor's Constant

Cutting Velocity

Cutting Velocity is the velocity at the periphery of the cutter or workpiece (whichever is rotating).

Symbol: V

Measurement: SpeedUnit: m/s

Note: Value should be greater than 0.

Formulas to find Cutting Velocity

Feed Rate

Feed Rate is defined as the tool's distance travelled during one spindle revolution.

Symbol: f

Measurement: FeedUnit: mm/rev

Note: Value should be greater than 0.

Formulas to find Feed Rate

Taylor's Exponent for Feed Rate in Taylors Theory

Taylor's Exponent for Feed Rate in Taylors Theory is an experimental exponent used to draw a relation between feed rate to workpiece and tool life.

Symbol: a

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Taylor's Exponent for Feed Rate in Taylors Theory

Maximum Tool Life

Maximum Tool Life is the period of time for which the cutting edge, affected by the cutting procedure, retains its cutting capacity between sharpening operations.

Symbol: L_max

Measurement: TimeUnit: s

Note: Value should be greater than 0.

Formulas to find Maximum Tool Life

Taylor Tool Life Exponent

Taylor Tool Life Exponent is an experimental exponent that helps in quantifying the rate of tool wear.

Symbol: y

Measurement: NAUnit: Unitless

Note: Value should be between 0 to 1.

Formulas to find Taylor Tool Life Exponent

Depth of Cut

Depth of Cut is the tertiary cutting motion that provides a necessary depth of material that is required to remove by machining. It is usually given in the third perpendicular direction.

Symbol: d

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Depth of Cut

The natural logarithm, also known as the logarithm to the base e, is the inverse function of the natural exponential function.

Syntax: ln(Number)

Other formulas in Taylor's Theory category

Go Taylor's Tool Life given Cutting Velocity and Intercept

T tl = {(\frac{C}{V})}^{\frac{1}{y}}

Go Taylor's Exponent if Ratios of Cutting Velocities, Tool Lives are given in Two Machining Conditions

y = (- 1) \cdot \frac{\ln (R v)}{\ln (R l)}

How to Evaluate Taylor's Exponent of Depth of Cut?

Taylor's Exponent of Depth of Cut evaluator uses Taylor's Exponent for Depth of Cut = ln(Taylor's Constant/(Cutting Velocity*(Feed Rate^Taylor's Exponent for Feed Rate in Taylors Theory)*(Maximum Tool Life^Taylor Tool Life Exponent)))/ln(Depth of Cut) to evaluate the Taylor's Exponent for Depth of Cut, Taylor's exponent of Depth of Cut is a method to determine the experimental exponent for Depth of Cut after practical data of tool machining have been tabulated. Taylor's Exponent for Depth of Cut is denoted by b symbol.

How to evaluate Taylor's Exponent of Depth of Cut using this online evaluator? To use this online evaluator for Taylor's Exponent of Depth of Cut, enter Taylor's Constant (C), Cutting Velocity (V), Feed Rate (f), Taylor's Exponent for Feed Rate in Taylors Theory (a), Maximum Tool Life (L_max), Taylor Tool Life Exponent (y) & Depth of Cut (d) and hit the calculate button.

FAQs on Taylor's Exponent of Depth of Cut

What is the formula to find Taylor's Exponent of Depth of Cut?

The formula of Taylor's Exponent of Depth of Cut is expressed as Taylor's Exponent for Depth of Cut = ln(Taylor's Constant/(Cutting Velocity*(Feed Rate^Taylor's Exponent for Feed Rate in Taylors Theory)*(Maximum Tool Life^Taylor Tool Life Exponent)))/ln(Depth of Cut). Here is an example- 0.239999 = ln(85.13059/(0.833333*(0.0007^0.2)*(4500^0.8466244)))/ln(0.013).

How to calculate Taylor's Exponent of Depth of Cut?

With Taylor's Constant (C), Cutting Velocity (V), Feed Rate (f), Taylor's Exponent for Feed Rate in Taylors Theory (a), Maximum Tool Life (L_max), Taylor Tool Life Exponent (y) & Depth of Cut (d) we can find Taylor's Exponent of Depth of Cut using the formula - Taylor's Exponent for Depth of Cut = ln(Taylor's Constant/(Cutting Velocity*(Feed Rate^Taylor's Exponent for Feed Rate in Taylors Theory)*(Maximum Tool Life^Taylor Tool Life Exponent)))/ln(Depth of Cut). This formula also uses Natural Logarithm (ln) function(s).

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Taylor's Exponent of Depth of Cut Formula

Taylor's Exponent of Depth of Cut Example

Taylor's Exponent of Depth of Cut Solution

Taylor's Exponent of Depth of Cut Formula Elements

Other formulas in Taylor's Theory category

How to Evaluate Taylor's Exponent of Depth of Cut?

FAQs on Taylor's Exponent of Depth of Cut

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