## Time Taken for Drive Speed Solution

STEP 0: Pre-Calculation Summary
Formula Used
Time Taken for Drive Speed = Moment of Inertia*int(1/(Torque-Load Torque),x,Initial angular Velocity,Final Angular Velocity)
t = J*int(1/(τ-τL),x,ωm1,ωm2)
This formula uses 1 Functions, 6 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
Time Taken for Drive Speed - (Measured in Second) - Time Taken for Drive Speed is Defined as the Time which Drive takes to Change its Velocity from ωm1 to ωm2.
Moment of Inertia - (Measured in Kilogram Square Meter) - Moment of Inertia is a measure of an object's resistance to changes in its rotational motion. It depends on the mass distribution of the object and its shape relative to the axis of rotation.
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.
Load Torque - (Measured in Newton Meter) - Load Torque is defined as the torque experienced by the load connected to the motor shaft. It can come from various sources, such as friction, gravitational forces, or external mechanical loads.
Initial angular Velocity - (Measured in Radian per Second) - Initial angular Velocity is defined as the rotational speed of the motor shaft at a specific starting point or initial condition.
Final Angular Velocity - (Measured in Radian per Second) - Final Angular Velocity is Defined as the Rotational Speed of the Motor Shaft at the Final or Resulting Point.
STEP 1: Convert Input(s) to Base Unit
Moment of Inertia: 10 Kilogram Square Meter --> 10 Kilogram Square Meter No Conversion Required
Torque: 5.4 Newton Meter --> 5.4 Newton Meter No Conversion Required
Load Torque: 0.235 Newton Meter --> 0.235 Newton Meter No Conversion Required
Initial angular Velocity: 2.346 Radian per Second --> 2.346 Radian per Second No Conversion Required
Final Angular Velocity: 4.675 Radian per Second --> 4.675 Radian per Second No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
t = J*int(1/(τ-τL),x,ωm1m2) --> 10*int(1/(5.4-0.235),x,2.346,4.675)
Evaluating ... ...
t = 4.50919651500484
STEP 3: Convert Result to Output's Unit
4.50919651500484 Second --> No Conversion Required
4.50919651500484 4.509197 Second <-- Time Taken for Drive Speed
(Calculation completed in 00.004 seconds)
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## Credits

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
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
Torque = (Constant*Voltage^2*Rotor Resistance)/((Stator Resistance+Rotor Resistance)^2+(Stator Reactance+Rotor Reactance)^2)
Torque Generated by Scherbius Drive
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
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
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
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
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
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
DC Voltage = (3*sqrt(2))*(RMS Value of Rotor Side Line Voltage/pi)
Gear Tooth Ratio
Gear Tooth Ratio = Number 1 of Teeth of Driving Gear/Number 2 of Teeth of Driven Gear
Average Back Emf with Negligible Commutation Overlap
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
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 Voltage = 3*(Peak Voltage/pi)

## Time Taken for Drive Speed Formula

Time Taken for Drive Speed = Moment of Inertia*int(1/(Torque-Load Torque),x,Initial angular Velocity,Final Angular Velocity)
t = J*int(1/(τ-τL),x,ωm1,ωm2)

## Explain How Changes in Torque Impact the Transient Time of an Electric Drive System?

Changes in torque directly impact the transient time of an electric drive system. When torque changes suddenly, the system's angular velocity responds accordingly, either accelerating or decelerating the load. The system's moment of inertia determines how quickly it can adjust to these torque changes, with higher inertia leading to slower responses. Overall, torque changes influence how rapidly the system reaches a new steady-state condition, with larger changes resulting in quicker adaptation and smaller changes indicating slower adjustment.

## How to Calculate Time Taken for Drive Speed?

Time Taken for Drive Speed calculator uses Time Taken for Drive Speed = Moment of Inertia*int(1/(Torque-Load Torque),x,Initial angular Velocity,Final Angular Velocity) to calculate the Time Taken for Drive Speed, The Time Taken for Drive Speed is defined as the time which Drive takes to Change its Velocity from ωm1 to ωm2. It represents the duration it takes for the system to transition from one state to another in response to a change in torque. Time Taken for Drive Speed is denoted by t symbol.

How to calculate Time Taken for Drive Speed using this online calculator? To use this online calculator for Time Taken for Drive Speed, enter Moment of Inertia (J), Torque (τ), Load Torque L), Initial angular Velocity m1) & Final Angular Velocity m2) and hit the calculate button. Here is how the Time Taken for Drive Speed calculation can be explained with given input values -> 4.509197 = 10*int(1/(5.4-0.235),x,2.346,4.675).

### FAQ

What is Time Taken for Drive Speed?
The Time Taken for Drive Speed is defined as the time which Drive takes to Change its Velocity from ωm1 to ωm2. It represents the duration it takes for the system to transition from one state to another in response to a change in torque and is represented as t = J*int(1/(τ-τL),x,ωm1m2) or Time Taken for Drive Speed = Moment of Inertia*int(1/(Torque-Load Torque),x,Initial angular Velocity,Final Angular Velocity). Moment of Inertia is a measure of an object's resistance to changes in its rotational motion. It depends on the mass distribution of the object and its shape relative to the axis of rotation, 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, Load Torque is defined as the torque experienced by the load connected to the motor shaft. It can come from various sources, such as friction, gravitational forces, or external mechanical loads, Initial angular Velocity is defined as the rotational speed of the motor shaft at a specific starting point or initial condition & Final Angular Velocity is Defined as the Rotational Speed of the Motor Shaft at the Final or Resulting Point.
How to calculate Time Taken for Drive Speed?
The Time Taken for Drive Speed is defined as the time which Drive takes to Change its Velocity from ωm1 to ωm2. It represents the duration it takes for the system to transition from one state to another in response to a change in torque is calculated using Time Taken for Drive Speed = Moment of Inertia*int(1/(Torque-Load Torque),x,Initial angular Velocity,Final Angular Velocity). To calculate Time Taken for Drive Speed, you need Moment of Inertia (J), Torque (τ), Load Torque L), Initial angular Velocity m1) & Final Angular Velocity m2). With our tool, you need to enter the respective value for Moment of Inertia, Torque, Load Torque, Initial angular Velocity & Final Angular Velocity 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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