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# Calculation of motor starting time as first approximation

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## Motor starting operations

The problems connected to motor starting operations are fundamentally linked to the type of motor which a determined motor operational torque “CM offers, to the starting modality and to the connected load which has a determined load torque “C ”.

The necessary starting torque “Ca can be expressed as:

Ca = CM – CL

and shall be well calibrated to prevent it from being either too low, so as starting is not too long and heavy – which causes risks of temperature rise for the motor – or from being too high on the joints or on the operating machines.

A generic curve of the above mentioned quantities is shown in the Figure 1 below.

The concept of motor starting time “ta” can be associated to this concept of properly calibrated starting and can be evaluated making reference to concepts linked to the motion dynamics, but also by introducing simplifying hypotheses which allows, however, an evaluation with a good approximation.

It is possible to relate the acceleration torque, expressed as a difference between the motor operational torque and the load torque, to the moment of inertia of the motor “JM, of the load “JL and to the motor angular speed, to obtain the following formula:

where the expression of “dω” assumes the following form:

and it is obtained by differentiating the well known expression for the motor angular speed:

Through simple mathematical operations and applying the method of integral calculus, it is possible to make the unknown quantity “ta” explicit by the following expression:

To express the value of the acceleration torque, it is necessary to introduce some simplifications:

The first one consists in considering an average value for the motor operational torque to be expressed as:

CM = 0.45 x (Cs + Cmax)

where CS represents the inrush torque and Cmax the maximum torque;

The second one concerns the torque due to the load and which can be correct by applying the multiplying factor KL linked to the load typology as in Table 1 below.

Table 1 – Values of factor KL

 Type of comparable loads Load Coefficient Lift Fans Piston Pumps Flywheel KL 1 0.33 0.5 0

In order to better understand the significance of the coefficient KL we associate to the type of load indicated in the table the torque characterizing the starting phase of the load by means of the following assumptions:

• Lift = load torque constant during acceleration
• Fans = load torque with square law increase during acceleration
• Piston pumps = load torque with linear increase during acceleration
• Flywheel = zero load torque.

With these assumptions, the acceleration torque can be expressed as:

These hypotheses allow to obtain the motor starting time with the aid of the following formula

The starting time allows to define whether a normal or a heavy duty start must be realized and to choose correctly the protection and switching devices. The above mentioned parameters relevant to the motor are given by the manufacturer of the motor.

As an example, Table 2 below shows the values that these parameters can take for three-phase asynchronous motors of common use and typically present on the market. Obviously the parameters relevant to the load characterize each single application and must be known by the designer.

Table 2 – Typical values of some electrical and mechanical parameters of a three-phase asynchronous motor

## Calculation of the starting time of a motor

Making reference to the data of the above table, here is an example of calculation of the starting time of a motor, according to the theoretical treatment previously developed.

 Three-phase asynchronous motor – 4 poles Frequency 160 kW Frequency 50 Hz Rated speed 1500 rpm Speed at full load 1487 rpm Moment of inertia of the motor JM = 2.9 Kgm2 Moment of inertia of the load JL = 60 Kgm2 Load torque CL = 1600 Nm Rated torque of the motor CN = 1028 Nm Inrush torque Cs = 2467 Nm (Cs = 2.4 x 1028) Max. torque Cmax = 2981 Nm (Cmax = 2.9 x 1028) Load with constant torque KL = 1

Cacc = 0.45 · ( CS + Cmax) – KL· CL = 0.45 · (2467 + 2981) – (1 · 1600) = 851.6 Nm

from which
ta = (2 · π · 1500 · (2.9 + 60)) / 60 · 851.6 = 11.6 s

Cacc = 0.45 · ( CS + Cmax) – K· CL = 0.45 · (2467 + 2981) – (0.33 · 1600) = 1923.6 Nm

from which
ta = (2 · π · 1500 · (2.9 + 60)) / 60 · 1923.6 = 5.14 s

For both typologies of load, the esteemed motor starting time results to comply with the instruction given by the manufacturer regarding the maximum time admitted for DOL starting. This indication can be also taken as a cue for a correct evaluation of the thermal protection device to be chosen.

Reference // Three-phase asynchronous motors: generalities and proposals for the coordination of protective devices – ABB

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### Edvard Csanyi

Electrical engineer, programmer and founder of EEP. Highly specialized for design of LV/MV switchgears and LV high power busbar trunking (<6300A) in power substations, commercial buildings and industry facilities. Professional in AutoCAD programming.

1. Jon
Sep 14, 2019

Hi
I have some questions?
An electro motor with a liquid starter of 3 MW is available.
In the manual of equipping, Start method is Directly, Can You Get Started with Liquid Starter?
The type of load is the fan
How is the startup time calculating?
Thank you

2. mahmoud
Oct 30, 2015

are we take the starting current of motors in total load calculations in projects?

3. Ekanath
Oct 18, 2015

Good information and

Jul 15, 2015

I just want to know that how to increase the starting torque of a 130kw dc motor (series and compound).thanx

5. st01
Jun 23, 2015

thank you

6. saibaba
Jun 23, 2015

I am working in a chilar plant there v use vfds
One problem occurs while motor starting
It is starting with a abnormal sounds and vibration ager sum time it is getting to normal…..
Wht is the train for it

7. amine
Jun 23, 2015

thank you

Jun 23, 2015

If load torque is higher than motor torque will current taken by motor become higher and CB trip.

• Cherry Gupta
Dec 11, 2015

Starting current of a motor will certainly not depend on difference between motor torque and load torque. But definitely the starting time will be lower, larger the difference which is also known as accelerating torque. Now, if the circuit breaker (providing only short circuit protection) faces current beyond it’s time-current characteristics, definitely it will do it’s job and trip the circuit. This will defilitely happen if there is a locked rotor situation, when starting current will flow for longer duration (and not a normal start duration of say 5 to 7 secs). For extended starting time, you would need to choose a heavy duty starter, which gives a longer time to the motor to start successfully. I have a excel spreadsheet to calculate the starting time of a motor, with some data required from the driven load + motor as explained above. It’s a graphical cum spreadsheet method, triving to do exactly what has been explained above.

• Mufaro
Dec 06, 2017

Hi Cherry. Can you please share the excel spreadsheet to calculate the starting time of a motor, with some data required from the driven load + motor as explained above?

• Carlos Mendoza
Apr 07, 2018

Hi Cherry. Can you please share the excel spreadsheet to calculate the starting time of a motor,thank you, I write to you from Peru

Jun 23, 2015

please give starting time of induction motors of various kW & speed as we use mostly them not syn motors.

• Cherry Gupta
Dec 11, 2015

Hi Sri….the starting time is a calculation of rotational dynamics, involving the driving torque (motor torque), driven torque (load torque) and the rotating inertia (combined inertia of motor & load). As stated above, the calculation is for a asynchronous motor (which means this motor DOES NOT rotate at synchronous speed i.e it is an induction motor). Hope the above example is clear with you.