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|
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
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|
|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
ta = (2 · π · 1500 · (2.9 + 60)) / 60 · 851.6 = 11.6 s
Load with quadratic rising torque KL = 0.33
Cacc = 0.45 · ( CS + Cmax) – KL · CL = 0.45 · (2467 + 2981) – (0.33 · 1600) = 1923.6 Nm
ta = (2 · π · 1500 · (2.9 + 60)) / 60 · 1923.6 = 5.14 s
Reference // Three-phase asynchronous motors: generalities and proposals for the coordination of protective devices – ABB