Voltage of Power Supply from Average Power per Spark Calculator

✖Average power is defined as the ratio of total work done by the body to the total time taken by the body.ⓘ Average Power [P_avg]			+10% -10%
✖Resistance of the charging circuit avg pow is the resistance of the charging circuit.ⓘ Resistance of the Charging Circuit Avg Pow [R_av]			+10% -10%
✖Time for charging capacitor to breakdown voltage is denoted by τ.ⓘ Time for Charging Capacitor to Breakdown Voltage [τ_p]			+10% -10%
✖Time Constant avg pow is the response represents the elapsed time required for the system response to decay to zero if the system had continued to decay at the initial rate.ⓘ Time Constant Avg Pow [𝜏_av]			+10% -10%

✖Voltage of power supply Avg pow, is the voltage required to charge a given device within given time.ⓘ Voltage of Power Supply from Average Power per Spark [V_av]

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Formula

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Voltage of Power Supply from Average Power per Spark

Formula

`"V"_{"av"} = sqrt(("P"_{"avg"}*"R"_{"av"}*"τ"_{"p"})/("𝜏"_{"av"}*(1/2-exp(-"τ"_{"p"}/"𝜏"_{"av"})+0.5*exp(-2*"τ"_{"p"}/"𝜏"_{"av"}))))`

Example

`"10.03142V"=sqrt(("15.7J/s"*"0.181Ω"*"6.001s")/("100.1s"*(1/2-exp(-"6.001s"/"100.1s")+0.5*exp(-2*"6.001s"/"100.1s"))))`

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Voltage of Power Supply from Average Power per Spark Solution

STEP 0: Pre-Calculation Summary

Formula Used

Voltage of Power Supply Avg Pow = sqrt((Average Power*Resistance of the Charging Circuit Avg Pow*Time for Charging Capacitor to Breakdown Voltage)/(Time Constant Avg Pow*(1/2-exp(-Time for Charging Capacitor to Breakdown Voltage/Time Constant Avg Pow)+0.5*exp(-2*Time for Charging Capacitor to Breakdown Voltage/Time Constant Avg Pow))))
V_av = sqrt((P_avg*R_av*τ_p)/(𝜏_av*(1/2-exp(-τ_p/𝜏_av)+0.5*exp(-2*τ_p/𝜏_av))))
This formula uses 2 Functions, 5 Variables

Functions Used

exp - n an exponential function, the value of the function changes by a constant factor for every unit change in the independent variable., exp(Number)
sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)

Variables Used

Voltage of Power Supply Avg Pow - (Measured in Volt) - Voltage of power supply Avg pow, is the voltage required to charge a given device within given time.
Average Power - (Measured in Watt) - Average power is defined as the ratio of total work done by the body to the total time taken by the body.
Resistance of the Charging Circuit Avg Pow - (Measured in Ohm) - Resistance of the charging circuit avg pow is the resistance of the charging circuit.
Time for Charging Capacitor to Breakdown Voltage - (Measured in Second) - Time for charging capacitor to breakdown voltage is denoted by τ.
Time Constant Avg Pow - (Measured in Second) - Time Constant avg pow is the response represents the elapsed time required for the system response to decay to zero if the system had continued to decay at the initial rate.

STEP 1: Convert Input(s) to Base Unit

Average Power: 15.7 Joule per Second --> 15.7 Watt (Check conversion here)
Resistance of the Charging Circuit Avg Pow: 0.181 Ohm --> 0.181 Ohm No Conversion Required
Time for Charging Capacitor to Breakdown Voltage: 6.001 Second --> 6.001 Second No Conversion Required
Time Constant Avg Pow: 100.1 Second --> 100.1 Second No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

V_av = sqrt((P_avg*R_av*τ_p)/(𝜏_av*(1/2-exp(-τ_p/𝜏_av)+0.5*exp(-2*τ_p/𝜏_av)))) --> sqrt((15.7*0.181*6.001)/(100.1*(1/2-exp(-6.001/100.1)+0.5*exp(-2*6.001/100.1))))

Evaluating ... ...

V_av = 10.0314171574444

STEP 3: Convert Result to Output's Unit

10.0314171574444 Volt --> No Conversion Required

FINAL ANSWER

10.0314171574444 ≈ 10.03142 Volt <-- Voltage of Power Supply Avg Pow

(Calculation completed in 00.004 seconds)

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Home » Engineering » Production Engineering » Unconventional machining processes » Electro Discharge Machining (EDM) » System Analysis in EDM » Relaxation Circuit used for Generating Pulses in EDM » Average Power Delivered per Spark » Voltage of Power Supply from Average Power per Spark

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Created by Rajat Vishwakarma

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

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< 3 Average Power Delivered per Spark Calculators

Voltage of Power Supply from Average Power per Spark

Go Voltage of Power Supply Avg Pow = sqrt((Average Power*Resistance of the Charging Circuit Avg Pow*Time for Charging Capacitor to Breakdown Voltage)/(Time Constant Avg Pow*(1/2-exp(-Time for Charging Capacitor to Breakdown Voltage/Time Constant Avg Pow)+0.5*exp(-2*Time for Charging Capacitor to Breakdown Voltage/Time Constant Avg Pow))))

Resistance of Charging Circuit from Average Power per Spark

Go Resistance of the Charging Circuit Avg Pow = (Voltage of Power Supply Avg Pow^2*Time Constant Avg Pow)/(Average Power*Time for Charging Capacitor to Breakdown Voltage)*(1/2-exp(-Time for Charging Capacitor to Breakdown Voltage/Time Constant Avg Pow)+0.5*exp(-2*Time for Charging Capacitor to Breakdown Voltage/Time Constant Avg Pow))

Average Energy Delivered per Spark

Go Average Power = (Voltage of Power Supply Avg Pow^2*Time Constant Avg Pow)/(Resistance of the Charging Circuit Avg Pow*Time for Charging Capacitor to Breakdown Voltage)*(1/2-exp(-Time for Charging Capacitor to Breakdown Voltage/Time Constant Avg Pow)+0.5*exp(-2*Time for Charging Capacitor to Breakdown Voltage/Time Constant Avg Pow))

Voltage of Power Supply from Average Power per Spark 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 Voltage of Power Supply from Average Power per Spark?

Voltage of Power Supply from Average Power per Spark calculator uses Voltage of Power Supply Avg Pow = sqrt((Average Power*Resistance of the Charging Circuit Avg Pow*Time for Charging Capacitor to Breakdown Voltage)/(Time Constant Avg Pow*(1/2-exp(-Time for Charging Capacitor to Breakdown Voltage/Time Constant Avg Pow)+0.5*exp(-2*Time for Charging Capacitor to Breakdown Voltage/Time Constant Avg Pow)))) to calculate the Voltage of Power Supply Avg Pow, The Voltage of power supply from average power per spark formula is defined as the voltage of power supply used to charge the relaxation circuit used to provide spark in unconventional EDM. Voltage of Power Supply Avg Pow is denoted by V_av symbol.

How to calculate Voltage of Power Supply from Average Power per Spark using this online calculator? To use this online calculator for Voltage of Power Supply from Average Power per Spark, enter Average Power (P_avg), Resistance of the Charging Circuit Avg Pow (R_av), Time for Charging Capacitor to Breakdown Voltage (τ_p) & Time Constant Avg Pow (𝜏_av) and hit the calculate button. Here is how the Voltage of Power Supply from Average Power per Spark calculation can be explained with given input values -> 10.03142 = sqrt((15.7*0.181*6.001)/(100.1*(1/2-exp(-6.001/100.1)+0.5*exp(-2*6.001/100.1)))).

FAQ

What is Voltage of Power Supply from Average Power per Spark?

The Voltage of power supply from average power per spark formula is defined as the voltage of power supply used to charge the relaxation circuit used to provide spark in unconventional EDM and is represented as V_av = sqrt((P_avg*R_av*τ_p)/(𝜏_av*(1/2-exp(-τ_p/𝜏_av)+0.5*exp(-2*τ_p/𝜏_av)))) or Voltage of Power Supply Avg Pow = sqrt((Average Power*Resistance of the Charging Circuit Avg Pow*Time for Charging Capacitor to Breakdown Voltage)/(Time Constant Avg Pow*(1/2-exp(-Time for Charging Capacitor to Breakdown Voltage/Time Constant Avg Pow)+0.5*exp(-2*Time for Charging Capacitor to Breakdown Voltage/Time Constant Avg Pow)))). Average power is defined as the ratio of total work done by the body to the total time taken by the body, Resistance of the charging circuit avg pow is the resistance of the charging circuit, Time for charging capacitor to breakdown voltage is denoted by τ & Time Constant avg pow is the response represents the elapsed time required for the system response to decay to zero if the system had continued to decay at the initial rate.

How to calculate Voltage of Power Supply from Average Power per Spark?

The Voltage of power supply from average power per spark formula is defined as the voltage of power supply used to charge the relaxation circuit used to provide spark in unconventional EDM is calculated using Voltage of Power Supply Avg Pow = sqrt((Average Power*Resistance of the Charging Circuit Avg Pow*Time for Charging Capacitor to Breakdown Voltage)/(Time Constant Avg Pow*(1/2-exp(-Time for Charging Capacitor to Breakdown Voltage/Time Constant Avg Pow)+0.5*exp(-2*Time for Charging Capacitor to Breakdown Voltage/Time Constant Avg Pow)))). To calculate Voltage of Power Supply from Average Power per Spark, you need Average Power (P_avg), Resistance of the Charging Circuit Avg Pow (R_av), Time for Charging Capacitor to Breakdown Voltage (τ_p) & Time Constant Avg Pow (𝜏_av). With our tool, you need to enter the respective value for Average Power, Resistance of the Charging Circuit Avg Pow, Time for Charging Capacitor to Breakdown Voltage & Time Constant Avg Pow 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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