Proportionality constant for MRR Calculator

✖Material Removal Rate is the rate at which the material is removed from the work metal.ⓘ Material Removal Rate [MRR]			+10% -10%
✖Resistance of the charging circuit is the resistance of the charging circuit.ⓘ Resistance of the Charging Circuit [R_c]			+10% -10%
✖Voltage at any time t is the charging voltage in the circuit at any given time.ⓘ Voltage at any Time t [V_c]			+10% -10%
✖Voltage of power supply is the voltage required to charge a given device within given time.ⓘ Voltage of Power Supply [V₀]			+10% -10%

✖Proportionality constant of MRR is a proportionality constant defined to calculate MRR.ⓘ Proportionality constant for MRR [K_mrr]

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Formula

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Proportionality constant for MRR

Formula

`"K"_{"mrr"} = -("MRR"*(2*"R"_{"c"}*ln(1-("V"_{"c"}/"V"_{"0"}))))/"V"_{"c"}^2`

Example

`"1.499993"=-("74690g/s"*(2*"0.18Ω"*ln(1-("2V"/"10V"))))/("2V")^2`

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Proportionality constant for MRR Solution

STEP 0: Pre-Calculation Summary

Formula Used

Proportionality Constant of MRR = -(Material Removal Rate*(2*Resistance of the Charging Circuit*ln(1-(Voltage at any Time t/Voltage of Power Supply))))/Voltage at any Time t^2
K_mrr = -(MRR*(2*R_c*ln(1-(V_c/V₀))))/V_c^2
This formula uses 1 Functions, 5 Variables

Functions Used

ln - The natural logarithm, also known as the logarithm to the base e, is the inverse function of the natural exponential function., ln(Number)

Variables Used

Proportionality Constant of MRR - Proportionality constant of MRR is a proportionality constant defined to calculate MRR.
Material Removal Rate - (Measured in Kilogram per Second) - Material Removal Rate is the rate at which the material is removed from the work metal.
Resistance of the Charging Circuit - (Measured in Ohm) - Resistance of the charging circuit is the resistance of the charging circuit.
Voltage at any Time t - (Measured in Volt) - Voltage at any time t is the charging voltage in the circuit at any given time.
Voltage of Power Supply - (Measured in Volt) - Voltage of power supply is the voltage required to charge a given device within given time.

STEP 1: Convert Input(s) to Base Unit

Material Removal Rate: 74690 Gram per Second --> 74.69 Kilogram per Second (Check conversion here)
Resistance of the Charging Circuit: 0.18 Ohm --> 0.18 Ohm No Conversion Required
Voltage at any Time t: 2 Volt --> 2 Volt No Conversion Required
Voltage of Power Supply: 10 Volt --> 10 Volt No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

K_mrr = -(MRR*(2*R_c*ln(1-(V_c/V₀))))/V_c^2 --> -(74.69*(2*0.18*ln(1-(2/10))))/2^2

Evaluating ... ...

K_mrr = 1.49999326628925

STEP 3: Convert Result to Output's Unit

1.49999326628925 --> No Conversion Required

FINAL ANSWER

1.49999326628925 ≈ 1.499993 <-- Proportionality Constant of MRR

(Calculation completed in 00.004 seconds)

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University Institute of Technology RGPV (UIT - RGPV), Bhopal

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< 7 Material removal rate (MRR) Calculators

Proportionality constant for MRR

Go Proportionality Constant of MRR = -(Material Removal Rate*(2*Resistance of the Charging Circuit*ln(1-(Voltage at any Time t/Voltage of Power Supply))))/Voltage at any Time t^2

Material removal rate, MRR

Go Material Removal Rate = -(Proportionality Constant of MRR*Voltage at any Time t^2)/(2*Resistance of the Charging Circuit*ln(1-(Voltage at any Time t/Voltage of Power Supply)))

Resistance of circuit

Go Resistance of the Charging Circuit = -(Proportionality Constant of MRR*Voltage at any Time t^2)/(2*Material Removal Rate*ln(1-(Voltage at any Time t/Voltage of Power Supply)))

Input power supply to achieve given MRR

Go Voltage of Power Supply = Voltage at any Time t/(1-exp(-(Proportionality Constant of MRR*Voltage at any Time t^2)/(2*Resistance of the Charging Circuit*Metal Removal Rate)))

Metal removal rate from volume of crater

Go Metal Removal Rate = Volume of Crater*Frequency of Charging

Frequency of charging from volume crater

Go Frequency of Charging = Metal Removal Rate/Volume of Crater

Volume of crater from MRR

Go Volume of Crater = Metal Removal Rate/Frequency of Charging

Proportionality constant for MRR Formula

How the spark is produced in Electric Discharge Machining ?

A typical circuit used for supplying the power to an EDM machine is named as the relaxation circuit. The circuit consists of a DC power source, which charges the capacitor ‘C’ across a resistance ‘Rc’. Initially when the capacitor is in the uncharged condition, when the power supply is on with a voltage of Vo, a heavy current, ic, will flow in the circuit as shown to charge the capacitor. The relaxation circuit as explained above was used in the early EDM machines. They are limited to the low material removal rates for fine finish, which limits its application. This can be explained from the fact that the time spent on charging the capacitor is quite large during which time, no machining can actually take place. Thus the material removal rates are low.

How to Calculate Proportionality constant for MRR?

Proportionality constant for MRR calculator uses Proportionality Constant of MRR = -(Material Removal Rate*(2*Resistance of the Charging Circuit*ln(1-(Voltage at any Time t/Voltage of Power Supply))))/Voltage at any Time t^2 to calculate the Proportionality Constant of MRR, The Proportionality constant for MRR formula is defined as the constant introduced to remove the proportionality from MRR equation. Proportionality Constant of MRR is denoted by K_mrr symbol.

How to calculate Proportionality constant for MRR using this online calculator? To use this online calculator for Proportionality constant for MRR, enter Material Removal Rate (MRR), Resistance of the Charging Circuit (R_c), Voltage at any Time t (V_c) & Voltage of Power Supply (V₀) and hit the calculate button. Here is how the Proportionality constant for MRR calculation can be explained with given input values -> 5.8E-6 = -(74.69*(2*0.18*ln(1-(2/10))))/2^2.

FAQ

What is Proportionality constant for MRR?

The Proportionality constant for MRR formula is defined as the constant introduced to remove the proportionality from MRR equation and is represented as K_mrr = -(MRR*(2*R_c*ln(1-(V_c/V₀))))/V_c^2 or Proportionality Constant of MRR = -(Material Removal Rate*(2*Resistance of the Charging Circuit*ln(1-(Voltage at any Time t/Voltage of Power Supply))))/Voltage at any Time t^2. Material Removal Rate is the rate at which the material is removed from the work metal, Resistance of the charging circuit is the resistance of the charging circuit, Voltage at any time t is the charging voltage in the circuit at any given time & Voltage of power supply is the voltage required to charge a given device within given time.

How to calculate Proportionality constant for MRR?

The Proportionality constant for MRR formula is defined as the constant introduced to remove the proportionality from MRR equation is calculated using Proportionality Constant of MRR = -(Material Removal Rate*(2*Resistance of the Charging Circuit*ln(1-(Voltage at any Time t/Voltage of Power Supply))))/Voltage at any Time t^2. To calculate Proportionality constant for MRR, you need Material Removal Rate (MRR), Resistance of the Charging Circuit (R_c), Voltage at any Time t (V_c) & Voltage of Power Supply (V₀). With our tool, you need to enter the respective value for Material Removal Rate, Resistance of the Charging Circuit, Voltage at any Time t & Voltage of Power Supply and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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