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Constant for machine type b given Machining time for maximum power Formula

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Constant For Tool Type(b) is defined as the constant for the type of material used in the tool. Check FAQs

b = 1 - \frac{\ln (ρ \cdot a \cdot t p) - \ln (V 0 \cdot p s)}{\ln (W)}

b - Constant For Tool Type(b)?ρ - Density of Work Piece?a - Constant For Tool Type(a)?t_p - Machining Time For Maximum Power?V₀ - Proportion of Initial Volume?p_s - Specific Cutting Energy in Machining?W - Initial Work Piece Weight?

Constant for machine type b given Machining time for maximum power Example

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Here is how the Constant for machine type b given Machining time for maximum power equation looks like with Values.

Here is how the Constant for machine type b given Machining time for maximum power equation looks like with Units.

Here is how the Constant for machine type b given Machining time for maximum power equation looks like.

0.53 = 1 - \frac{\ln (7850 \cdot 2.9 \cdot 48.925) - \ln (0.0001 \cdot 3000.487)}{\ln (12.8)}

0.53 = 1 - \frac{\ln (7850kg/m³ \cdot 2.9 \cdot 48.925s) - \ln (0.0001 \cdot 3000.487MJ/m³)}{\ln (12.8kg)}

0.53 = 1 - \frac{\ln (7850 \cdot 2.9 \cdot 48.925) - \ln (0.0001 \cdot 3000.487)}{\ln (12.8)}

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Constant for machine type b given Machining time for maximum power Solution

Follow our step by step solution on how to calculate Constant for machine type b given Machining time for maximum power?

FIRST Step Consider the formula

b = 1 - \frac{\ln (ρ \cdot a \cdot t p) - \ln (V 0 \cdot p s)}{\ln (W)}

Next Step Substitute values of Variables

∴

b = 1 - \frac{\ln (7850kg/m³ \cdot 2.9 \cdot 48.925s) - \ln (0.0001 \cdot 3000.487MJ/m³)}{\ln (12.8kg)}

Next Step Convert Units

∴

b = 1 - \frac{\ln (7850kg/m³ \cdot 2.9 \cdot 48.925s) - \ln (0.0001 \cdot 3E+9J/m³)}{\ln (12.8kg)}

Next Step Prepare to Evaluate

∴

b = 1 - \frac{\ln (7850 \cdot 2.9 \cdot 48.925) - \ln (0.0001 \cdot 3E+9)}{\ln (12.8)}

Next Step Evaluate

∴

b = 0.529999827884223

LAST Step Rounding Answer

∴

b = 0.53

Constant for machine type b given Machining time for maximum power Formula Elements

Variables

Functions

Constant For Tool Type(b)

Constant For Tool Type(b) is defined as the constant for the type of material used in the tool.

Symbol: b

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Constant For Tool Type(b)

Density of Work Piece

The Density of Work Piece is the mass per unit volume ratio of the material of workpiece.

Symbol: ρ

Measurement: DensityUnit: kg/m³

Note: Value should be greater than 0.

Formulas to find Density of Work Piece

Constant For Tool Type(a)

Constant For Tool Type(a) is defined as the constant for the type of material used in the tool.

Symbol: a

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Constant For Tool Type(a)

Machining Time For Maximum Power

Machining Time For Maximum Power is the time for processing when the workpiece is machined under maximum power conditions.

Symbol: t_p

Measurement: TimeUnit: s

Note: Value should be greater than 0.

Formulas to find Machining Time For Maximum Power

Proportion of Initial Volume

The Proportion of Initial Volume or weight is the proportion of initial volume or initial weight to be removed by machining.

Symbol: V₀

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Proportion of Initial Volume

Specific Cutting Energy in Machining

Specific Cutting Energy in Machining is the energy consumed to remove a unit volume of material, which is calculated as the ratio of cutting energy e to material removal volume v.

Symbol: p_s

Measurement: Energy DensityUnit: MJ/m³

Note: Value should be greater than 0.

Formulas to find Specific Cutting Energy in Machining

Initial Work Piece Weight

Initial Work Piece Weight is defined as the weight of the work piece before undergoing machining operation.

Symbol: W

Measurement: WeightUnit: kg

Note: Value should be greater than 0.

Formulas to find Initial Work Piece Weight

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 Machining Time category

Go Time Proportion of Cutting Edge Engagement for Maximum Power delivery given Machining Cost

Q = T \cdot \frac{(\frac{C m}{t p}) - M}{M \cdot t c + C t}

Go Machining Time for Maximum Power given Machining Cost

t p = \frac{C m}{M + (Q \cdot \frac{M \cdot t c + C t}{T})}

How to Evaluate Constant for machine type b given Machining time for maximum power?

Constant for machine type b given Machining time for maximum power evaluator uses Constant For Tool Type(b) = 1-(ln(Density of Work Piece*Constant For Tool Type(a)*Machining Time For Maximum Power)-ln(Proportion of Initial Volume*Specific Cutting Energy in Machining))/ln(Initial Work Piece Weight) to evaluate the Constant For Tool Type(b), The Constant for machine type b given Machining time for maximum power is defined as the constant for the type of material used in the tool. Constant For Tool Type(b) is denoted by b symbol.

How to evaluate Constant for machine type b given Machining time for maximum power using this online evaluator? To use this online evaluator for Constant for machine type b given Machining time for maximum power, enter Density of Work Piece (ρ), Constant For Tool Type(a) (a), Machining Time For Maximum Power (t_p), Proportion of Initial Volume (V₀), Specific Cutting Energy in Machining (p_s) & Initial Work Piece Weight (W) and hit the calculate button.

FAQs on Constant for machine type b given Machining time for maximum power

What is the formula to find Constant for machine type b given Machining time for maximum power?

The formula of Constant for machine type b given Machining time for maximum power is expressed as Constant For Tool Type(b) = 1-(ln(Density of Work Piece*Constant For Tool Type(a)*Machining Time For Maximum Power)-ln(Proportion of Initial Volume*Specific Cutting Energy in Machining))/ln(Initial Work Piece Weight). Here is an example- 0.53 = 1-(ln(7850*2.9*48.925)-ln(0.000112*3000487000))/ln(12.79999).

How to calculate Constant for machine type b given Machining time for maximum power?

With Density of Work Piece (ρ), Constant For Tool Type(a) (a), Machining Time For Maximum Power (t_p), Proportion of Initial Volume (V₀), Specific Cutting Energy in Machining (p_s) & Initial Work Piece Weight (W) we can find Constant for machine type b given Machining time for maximum power using the formula - Constant For Tool Type(b) = 1-(ln(Density of Work Piece*Constant For Tool Type(a)*Machining Time For Maximum Power)-ln(Proportion of Initial Volume*Specific Cutting Energy in Machining))/ln(Initial Work Piece Weight). This formula also uses Natural Logarithm (ln) function(s).

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Constant for machine type b given Machining time for maximum power Formula

Constant for machine type b given Machining time for maximum power Example

Constant for machine type b given Machining time for maximum power Solution

Constant for machine type b given Machining time for maximum power Formula Elements

Other formulas in Machining Time category

How to Evaluate Constant for machine type b given Machining time for maximum power?

FAQs on Constant for machine type b given Machining time for maximum power

Variable Name