Torque generated by Scherbius Drive Solution

STEP 0: Pre-Calculation Summary
Formula Used
Torque = 1.35*((Average back emf voltage*Ac line voltage*Rectified Rotor Current*RMS value of Rotor side line voltage)/(Average back emf voltage*Angular Frequency))
TS = 1.35*((Eb*EL*Id*Er)/(Eb*ωs))
This formula uses 6 Variables
Variables Used
Torque - (Measured in Newton Meter) - Torque is described as the turning effect of force on the axis of rotation. In brief, it is a moment of force. It is characterized by τ.Torque is a vector quantity.
Average back emf voltage - (Measured in Volt) - Average back emf voltage the back emf is calculated based on the difference between the supplied voltage and the loss from the current through the resistance.
Ac line voltage - (Measured in Volt) - Ac line voltage is voltage between the two legs (called phase to phase or line to line) is 240V and the phase to neutral voltage is 120V.
Rectified Rotor Current - (Measured in Ampere) - Rectified Rotor Current which in turn is equal to the difference between the rectified Rotor voltage andthe average back e.m.f of the inverter divided by the resistance of the DC link Inductor.
RMS value of Rotor side line voltage - (Measured in Volt) - RMS value of Rotor side line voltage in static scherbius drive.
Angular Frequency - (Measured in Hertz) - Angular Frequency of a steadily recurring phenomenon expressed in radians per second.
STEP 1: Convert Input(s) to Base Unit
Average back emf voltage: 159.538 Volt --> 159.538 Volt No Conversion Required
Ac line voltage: 120 Volt --> 120 Volt No Conversion Required
Rectified Rotor Current: 2.2 Ampere --> 2.2 Ampere No Conversion Required
RMS value of Rotor side line voltage: 156 Volt --> 156 Volt No Conversion Required
Angular Frequency: 10.28 Revolution per Second --> 10.28 Hertz (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
TS = 1.35*((Eb*EL*Id*Er)/(Ebs)) --> 1.35*((159.538*120*2.2*156)/(159.538*10.28))
Evaluating ... ...
TS = 5408.4046692607
STEP 3: Convert Result to Output's Unit
5408.4046692607 Newton Meter --> No Conversion Required
FINAL ANSWER
5408.4046692607 Newton Meter <-- Torque
(Calculation completed in 00.016 seconds)

Credits

Created by Parminder Singh
Chandigarh University (CU), Punjab
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Verified by Aman Dhussawat
GURU TEGH BAHADUR INSTITUTE OF TECHNOLOGY (GTBIT), NEW DELHI
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8 Electric Drives Calculators

Torque generated by Scherbius Drive

Torque generated by Scherbius Drive

Formula
`"T"_{"S"} = 1.35*(("E"_{"b"}*"E"_{"L"}*"I"_{"d"}*"E"_{"r"})/("E"_{"b"}*"ω"_{"s"}))`

Example
`"5408.405N*m"=1.35*(("159.538V"*"120V"*"2.2A"*"156V")/("159.538V"*"10.28r/s"))`

Calculator
LaTeX
Go Torque = 1.35*((Average back emf voltage*Ac line voltage*Rectified Rotor Current*RMS value of Rotor side line voltage)/(Average back emf voltage*Angular Frequency))
Torque of Squirrel Cage Induction Motor

Torque of Squirrel Cage Induction Motor

Formula
`"T"_{"S"} = ("K"*("V"^2)*"R"_{"L"}) /(("R"_{"1"}+"R"_{"L"})^2+("X"_{"1"}+"X"_{"L"})^2)`

Example
`"5.485431N*m"=("0.11"*("200V"^2)*"10.1Ω") /(("11Ω"+"10.1Ω")^2+("42.5Ω"+"45Ω")^2)`

Calculator
LaTeX
Go Torque = (Constant*(Voltage^2)*Rotor resistance) /((Resistance+Rotor resistance)^2+(Stator reactance+Rotor reactance)^2)
Slip of Scherbius Drive given RMS Line Voltage

Slip of Scherbius Drive given RMS Line Voltage

Formula
`"s" = ("E"_{"b"}/"E"_{"r"})*"modulus"(cos("α"))`

Example
`"1.007143"=("159.538V"/"156V")*"modulus"(cos("10°"))`

Calculator
LaTeX
Go Slip = (Average back emf voltage/RMS value of Rotor side line voltage)*modulus(cos(Firing angle))
DC Output Voltage of Rectifier in Scherbius drive given Rotor RMS Line Voltage

DC Output Voltage of Rectifier in Scherbius drive given Rotor RMS Line Voltage

Formula
`"E"_{"DC"} = (3*sqrt(2))*("E"_{"r"}/pi)`

Example
`"210.674V"=(3*sqrt(2))*("156V"/pi)`

Calculator
LaTeX
Go DC Voltage = (3*sqrt(2))*(RMS value of Rotor side line voltage/pi)
Average Back emf with negligible commutation overlap

Average Back emf with negligible commutation overlap

Formula
`"E"_{"b"} = 1.35*"E"_{"L"}*cos("α") `

Example
`"159.5389V"=1.35*"120V"*cos("10°") `

Calculator
LaTeX
Go Average back emf voltage = 1.35*Ac line voltage*cos(Firing angle)
Gear Tooth Ratio

Gear Tooth Ratio

Formula
`"a" = ("n"_{"1"}/"n"_{"2"})`

Example
`"3"=("60"/"20")`

Calculator
LaTeX
Go Gear Tooth Ratio = (No. of Teeth of Driving Gear/No. of Teeth of Driven Gear)
DC Output Voltage of Rectifier in Scherbius drive given Rotor RMS Line Voltage at Slip

DC Output Voltage of Rectifier in Scherbius drive given Rotor RMS Line Voltage at Slip

Formula
`"E"_{"DC"} = 1.35*"E"_{"rs"}`

Example
`"210.897V"=1.35*"156.22V"`

Calculator
LaTeX
Go DC Voltage = 1.35*RMS value of Rotor side line voltage with slip
DC Output Voltage of Rectifier in Scherbius drive given Maximum Rotor Voltage

DC Output Voltage of Rectifier in Scherbius drive given Maximum Rotor Voltage

Formula
`"E"_{"DC"} = 3*("E"_{"rm"}/pi)`

Example
`"210.0845V"=3*("220V"/pi)`

Calculator
LaTeX
Go DC Voltage = 3*(Peak Voltage/pi)

Torque generated by Scherbius Drive Formula

Torque = 1.35*((Average back emf voltage*Ac line voltage*Rectified Rotor Current*RMS value of Rotor side line voltage)/(Average back emf voltage*Angular Frequency))
TS = 1.35*((Eb*EL*Id*Er)/(Eb*ωs))

What are some features of Scherbius drive?

Since power is fed back to the source, unlike in rotor resistance control where it is wasted in external resistors, drive has a high efficiency. The efficiency is even higher than the static voltage control for the same reason.
Drive Input power is the difference between motor input power and the power fed back. Reactive power is the sum of the motor and inverter reactive powers. Therefore this drive has a poor power factor throughout its range of operation.

How to Calculate Torque generated by Scherbius Drive?

Torque generated by Scherbius Drive calculator uses Torque = 1.35*((Average back emf voltage*Ac line voltage*Rectified Rotor Current*RMS value of Rotor side line voltage)/(Average back emf voltage*Angular Frequency)) to calculate the Torque, The Torque generated by Scherbius Drive formula is defined as steady state torque which is proportional to the rectified Rotor current which in turn is equal to the difference between the rectified Rotor voltage and the average back e.m.f of the inverter divided by the resistance of the DC link Inductor. Torque is denoted by TS symbol.

How to calculate Torque generated by Scherbius Drive using this online calculator? To use this online calculator for Torque generated by Scherbius Drive, enter Average back emf voltage (Eb), Ac line voltage (EL), Rectified Rotor Current (Id), RMS value of Rotor side line voltage (Er) & Angular Frequency s) and hit the calculate button. Here is how the Torque generated by Scherbius Drive calculation can be explained with given input values -> 5408.405 = 1.35*((159.538*120*2.2*156)/(159.538*10.28)).

FAQ

What is Torque generated by Scherbius Drive?
The Torque generated by Scherbius Drive formula is defined as steady state torque which is proportional to the rectified Rotor current which in turn is equal to the difference between the rectified Rotor voltage and the average back e.m.f of the inverter divided by the resistance of the DC link Inductor and is represented as TS = 1.35*((Eb*EL*Id*Er)/(Eb*ωs)) or Torque = 1.35*((Average back emf voltage*Ac line voltage*Rectified Rotor Current*RMS value of Rotor side line voltage)/(Average back emf voltage*Angular Frequency)). Average back emf voltage the back emf is calculated based on the difference between the supplied voltage and the loss from the current through the resistance, Ac line voltage is voltage between the two legs (called phase to phase or line to line) is 240V and the phase to neutral voltage is 120V, Rectified Rotor Current which in turn is equal to the difference between the rectified Rotor voltage andthe average back e.m.f of the inverter divided by the resistance of the DC link Inductor, RMS value of Rotor side line voltage in static scherbius drive & Angular Frequency of a steadily recurring phenomenon expressed in radians per second.
How to calculate Torque generated by Scherbius Drive?
The Torque generated by Scherbius Drive formula is defined as steady state torque which is proportional to the rectified Rotor current which in turn is equal to the difference between the rectified Rotor voltage and the average back e.m.f of the inverter divided by the resistance of the DC link Inductor is calculated using Torque = 1.35*((Average back emf voltage*Ac line voltage*Rectified Rotor Current*RMS value of Rotor side line voltage)/(Average back emf voltage*Angular Frequency)). To calculate Torque generated by Scherbius Drive, you need Average back emf voltage (Eb), Ac line voltage (EL), Rectified Rotor Current (Id), RMS value of Rotor side line voltage (Er) & Angular Frequency s). With our tool, you need to enter the respective value for Average back emf voltage, Ac line voltage, Rectified Rotor Current, RMS value of Rotor side line voltage & Angular Frequency and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
How many ways are there to calculate Torque?
In this formula, Torque uses Average back emf voltage, Ac line voltage, Rectified Rotor Current, RMS value of Rotor side line voltage & Angular Frequency. We can use 1 other way(s) to calculate the same, which is/are as follows -
  • Torque = (Constant*(Voltage^2)*Rotor resistance) /((Resistance+Rotor resistance)^2+(Stator reactance+Rotor reactance)^2)
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