Starting Time for Induction Motor under No Load Calculator

✖Mechanical Time Constant of Motor is Defined as the Time Taken by Motor to Reach its Synchronous Speed from Standstill Under Constant Accelerating Torque Equal to the Maximum Torque of the Motor.ⓘ Mechanical Time Constant of Motor [τ_m]			+10% -10%
✖Slip Energy Recovery is one of the methods of controlling the speed of an Induction motor.ⓘ Slip [s]			+10% -10%
✖Slip at Maximum Torque refers is the Slip Value at Which the Motor Produces its Highest Torque While still Maintaining a Stable Operating Condition.ⓘ Slip at Maximum Torque [s_m]			+10% -10%

✖The Starting Time for Induction Motor on No Load Refers to the Duration it Takes for the Motor to Accelerate from Rest to its Rated Speed When There is No Mechanical Load Applied to the Shaft.ⓘ Starting Time for Induction Motor under No Load [t_s]

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Formula

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Starting Time for Induction Motor under No Load

Formula

`"t"_{"s"} = (-"τ"_{"m"}/2)*int(("s"/"s"_{"m"}+"s"_{"m"}/"s")*x,x,1,0.05)`

Example

`"1.203632s"=(-"2.359s"/2)*int(("0.83"/"0.67"+"0.67"/"0.83")*x,x,1,0.05)`

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Starting Time for Induction Motor under No Load Solution

STEP 0: Pre-Calculation Summary

Formula Used

Starting Time For Induction motor on No Load = (-Mechanical Time Constant of Motor/2)*int((Slip/Slip at Maximum Torque+Slip at Maximum Torque/Slip)*x,x,1,0.05)
t_s = (-τ_m/2)*int((s/s_m+s_m/s)*x,x,1,0.05)
This formula uses 1 Functions, 4 Variables

Functions Used

int - The definite integral can be used to calculate net signed area, which is the area above the x -axis minus the area below the x -axis., int(expr, arg, from, to)

Variables Used

Starting Time For Induction motor on No Load - (Measured in Second) - The Starting Time for Induction Motor on No Load Refers to the Duration it Takes for the Motor to Accelerate from Rest to its Rated Speed When There is No Mechanical Load Applied to the Shaft.
Mechanical Time Constant of Motor - (Measured in Second) - Mechanical Time Constant of Motor is Defined as the Time Taken by Motor to Reach its Synchronous Speed from Standstill Under Constant Accelerating Torque Equal to the Maximum Torque of the Motor.
Slip - Slip Energy Recovery is one of the methods of controlling the speed of an Induction motor.
Slip at Maximum Torque - Slip at Maximum Torque refers is the Slip Value at Which the Motor Produces its Highest Torque While still Maintaining a Stable Operating Condition.

STEP 1: Convert Input(s) to Base Unit

Mechanical Time Constant of Motor: 2.359 Second --> 2.359 Second No Conversion Required
Slip: 0.83 --> No Conversion Required
Slip at Maximum Torque: 0.67 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

t_s = (-τ_m/2)*int((s/s_m+s_m/s)*x,x,1,0.05) --> (-2.359/2)*int((0.83/0.67+0.67/0.83)*x,x,1,0.05)

Evaluating ... ...

t_s = 1.2036324512228

STEP 3: Convert Result to Output's Unit

1.2036324512228 Second --> No Conversion Required

FINAL ANSWER

1.2036324512228 ≈ 1.203632 Second <-- Starting Time For Induction motor on No Load

(Calculation completed in 00.004 seconds)

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Created by Siddharth Raj

Heritage Institute of Technology ( HITK), Kolkata

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< 13 Electric Drives Calculators

Starting Time for Induction Motor under No Load

Go Starting Time For Induction motor on No Load = (-Mechanical Time Constant of Motor/2)*int((Slip/Slip at Maximum Torque+Slip at Maximum Torque/Slip)*x,x,1,0.05)

Torque of Squirrel Cage Induction Motor

Go Torque = (Constant*Voltage^2*Rotor Resistance)/((Stator Resistance+Rotor Resistance)^2+(Stator Reactance+Rotor Reactance)^2)

Torque Generated by Scherbius Drive

Go Torque = 1.35*((Back Emf*AC Line Voltage*Rectified Rotor Current*RMS Value of Rotor Side Line Voltage)/(Back Emf*Angular Frequency))

Time Taken for Drive Speed

Go Time Taken for Drive Speed = Moment of Inertia*int(1/(Torque-Load Torque),x,Initial angular Velocity,Final Angular Velocity)

Motor Terminal Voltage in Regenerative Braking

Go Motor Terminal Voltage = (1/Time Taken for Complete Operation)*int(Source Voltage*x,x,On-Period Time,Time Taken for Complete Operation)

Equivalent Current for Fluctuating and Intermittent Loads

Go Equivalent Current = sqrt((1/Time Taken for Complete Operation)*int((Electric Current)^2,x,1,Time Taken for Complete Operation))

Energy Dissipated during Transient Operation

Go Energy Dissipated in Transient Operation = int(Resistance of Motor Winding*(Electric Current)^2,x,0,Time Taken for Complete Operation)

Slip of Scherbius Drive given RMS Line Voltage

Go Slip = (Back Emf/RMS Value of Rotor Side Line Voltage)*modulus(cos(Firing Angle))

DC Output Voltage of Rectifier in Scherbius Drive Given Rotor RMS Line Voltage

Go DC Voltage = (3*sqrt(2))*(RMS Value of Rotor Side Line Voltage/pi)

Gear Tooth Ratio

Go Gear Tooth Ratio = Number 1 of Teeth of Driving Gear/Number 2 of Teeth of Driven Gear

Average Back Emf with Negligible Commutation Overlap

Go Back Emf = 1.35*AC Line Voltage*cos(Firing Angle)

DC Output Voltage of Rectifier in Scherbius Drive Given Rotor RMS Line Voltage at Slip

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

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

Starting Time for Induction Motor under No Load Formula

How does the Starting Time of an Induction Motor on No Load differs under Load Conditions?

The starting time of an induction motor on no load is typically shorter than its starting time under loaded conditions. This is because there is minimal resistance to the rotor's motion when starting on no load, allowing the motor to reach its rated speed more quickly. Conversely, starting under loaded conditions involves additional inertia and mechanical resistance, requiring more torque and time to overcome the load and reach the rated speed.

How to Calculate Starting Time for Induction Motor under No Load?

Starting Time for Induction Motor under No Load calculator uses Starting Time For Induction motor on No Load = (-Mechanical Time Constant of Motor/2)*int((Slip/Slip at Maximum Torque+Slip at Maximum Torque/Slip)*x,x,1,0.05) to calculate the Starting Time For Induction motor on No Load, The Starting Time for Induction Motor under No Load refers to the duration it takes for the motor to accelerate from rest to its rated speed when there is no mechanical load applied to the shaft. It characterizes the time required for the motor to reach its operating speed under no load conditions. Starting Time For Induction motor on No Load is denoted by t_s symbol.

How to calculate Starting Time for Induction Motor under No Load using this online calculator? To use this online calculator for Starting Time for Induction Motor under No Load, enter Mechanical Time Constant of Motor (τ_m), Slip (s) & Slip at Maximum Torque (s_m) and hit the calculate button. Here is how the Starting Time for Induction Motor under No Load calculation can be explained with given input values -> 1.203632 = (-2.359/2)*int((0.83/0.67+0.67/0.83)*x,x,1,0.05).

FAQ

What is Starting Time for Induction Motor under No Load?

The Starting Time for Induction Motor under No Load refers to the duration it takes for the motor to accelerate from rest to its rated speed when there is no mechanical load applied to the shaft. It characterizes the time required for the motor to reach its operating speed under no load conditions and is represented as t_s = (-τ_m/2)*int((s/s_m+s_m/s)*x,x,1,0.05) or Starting Time For Induction motor on No Load = (-Mechanical Time Constant of Motor/2)*int((Slip/Slip at Maximum Torque+Slip at Maximum Torque/Slip)*x,x,1,0.05). Mechanical Time Constant of Motor is Defined as the Time Taken by Motor to Reach its Synchronous Speed from Standstill Under Constant Accelerating Torque Equal to the Maximum Torque of the Motor, Slip Energy Recovery is one of the methods of controlling the speed of an Induction motor & Slip at Maximum Torque refers is the Slip Value at Which the Motor Produces its Highest Torque While still Maintaining a Stable Operating Condition.

How to calculate Starting Time for Induction Motor under No Load?

The Starting Time for Induction Motor under No Load refers to the duration it takes for the motor to accelerate from rest to its rated speed when there is no mechanical load applied to the shaft. It characterizes the time required for the motor to reach its operating speed under no load conditions is calculated using Starting Time For Induction motor on No Load = (-Mechanical Time Constant of Motor/2)*int((Slip/Slip at Maximum Torque+Slip at Maximum Torque/Slip)*x,x,1,0.05). To calculate Starting Time for Induction Motor under No Load, you need Mechanical Time Constant of Motor (τ_m), Slip (s) & Slip at Maximum Torque (s_m). With our tool, you need to enter the respective value for Mechanical Time Constant of Motor, Slip & Slip at Maximum Torque 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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