Static and dynamic characteristics of asynchronous motor.

Rieciciarova, Eva ; Nanasi, Tibor

Abstract: The paper presents experimental results and mathematical model of machine aggregates working under dynamic conditions. Generalized Kloss characteristics are derived for nominal operational speeds of 1,450 [min.sup.-1], 1,000 [min.sup.1] and 720 [min.sup.-1] under sinusoidal excitation. The steady-state motion presented as an ellipse centered at the working poin, which is intersection of moment characteristics of the asynchronous motor with the loading charateristics of DC motor with separate excitation. Measurements show, that it is necessary to consider the linear dynamic characteristics especially for dynamic response computations near to the resonance.

Key words: dynamic characteristics, dynamic testing, asynchronous motor, critical moment

1. INTRODUCTION

Experimental stand with the possibility of dynamic loading of machine aggregates and mechanisms (Fig. 1) enables to simula-te various cases of dynamic loading regimes with prescribed static and dynamic characteristics corresponding to production technological processes such as are the rolling, cutting, shearing, pressing, etc. The stand can be used for laboratory testing, production testing and examination, life testing and general tests of arbitrary mechatronic system or of mechanical sub-systems as are the gears, couplings, clutches, shafts, motors, etc (Mudrik & Nad 2008).

Another application is the investigation of energy and information flow through the electrical, pneumatic, hydraulic or mechanical subsystems of mechatronic system. Under mechatronic system we mean the integration of the electromechanical power subsystem with the electronic control subsystem to provide optimal regulation of the technological process or to provide optimal dynamic regime of the aggregate.

[FIGURE 1 OMITTED]

2. EXPERIMENTAL STAND

Experimental stand for dynamic loading of machine aggregates enables to investigate the influence of parameters of the aggregate on unevenness of the angular velocity [omega](t) or of the driving torque M(t). Also it is possible to obtain the dynamic characteristics of the machine aggregate in steady-state or in transient regime in the form of relationship M([omega]). The stand can help in assessment of capability of tested machine with respect to operational reliability, working accuracy and efficiency (Mudrik et al., 2008).

3. STEADY-STATE UNDER PERIOD-IC LOAD

Variation of parameters of aggregate (the inertia moment, fluctuating loads) gives rise to overall vibration, for which the unevenness of both the angular velocity and the driving torque is typical. As a result, the steady state appears in the form of the steady state motion.

The steady-state motion is characterised by closed trajectory of the form of an ellipse, depicted in detail on Fig. 2 together with it's characteristic points and with the corresponding linear static characteristics LSCH. Linear static characteristics is defined as tangent line at the working point [PHI].

4. EXPERIMENTAL MEASUREMENT

For analysis of dynamic properties of drives those properties are of importance, which influence the relations between input and output parameters of motor.

From measurement of the driving torque and of the slip (Table 1) the static moment characteristics of asynchronous motor was derived.

In general the static moment characteristics of asynchronous motor is described by the refined Kloss formula (Mudrik & Nad 2007).

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1)

where: s is the slip at the asynchronous speed,

[s.sub.k] is the critical slip corresponding to the critical moment [M.sub.dk].

a is the ratio of working resistances of stator and rotor.

The relation (1) was used to compute the characteristics for experimental results under sinusoidal loading with following detailed properties: [n.sub.d]=1000[min.sup.-1] (speed of asynchronous motor), [M.sub.dk] = 16.1 Nm (maximum moment), [s.sub.k] = 0,23 (critical slip) and a = 0 (ratio of working resistances of stator and rotor).

Using the above measured parameters allowed to find graphical presentation of the moment characteristics of asynchronous motor from Table 1 for rated revolutions [n.sub.d] = 720 [min.sup.-1] as well as from Table 2 for measurement at speed [n.sub.d] = 1 450 [min.sup.-1] .

The characteristics for the speed [n.sub.d] = 1 000 [min.sup.-1] was computed by the Kloss relation. In Fig. 3 all the three characteristics are compared.

The working point P([[omega].sub.[phi]], [M.sub.[phi]]) is the centre of the ellipse, corresponding to steady state motion. The working point is given as inter-section of the moment characteristics of asynchronous motor [M.sub.d]([[omega].sub.d]) with the characteristics [M.sub.z] ([[phi].sub.z], [[omega].sub.z]) of the loading torque of the DC motor (Nad 2007)..

[FIGURE 2 OMITTED]

5. CONCLUSION

The inertia moment and fluctuating loads give rise to vibration of aggregates. Resulting from unevenness of both the angular velocity and the driving torque the steady state appears in the form of the steady state motion. Electro-mechanical moment and the corresponding slip are of periodic nature and the asynchronous motor operates at so called "dynamic steady state".

As no resonance is developed increasing the inertia moment, the static moment characteristics can be used for computations in case of aggregates with constant transmission ratio.

When the static characteristics is used in computations, than for low rotational speeds the computed amplitude of driving moment underestimates the real value and for high rotational speeds the computed amplitude overestimates the real value. Therefore at least for frequencies in the vicinity of possible resonance the linear dynamic characteristics should be used instead of the static characteristics.

6. ACKNOWLEDGEMENTS

The results and such way also the contribution came into existence in connection with MS SR grant support of the project VEGA-1/0389/11.

7. REFERENCES

Mudrik, J., Nad', M. Principles of mechatronic modelling of machine aggregates. In Proceedings of International Conference "Theory and Practice of Gear Drives and Transmissions", Izevsk, Russia, 2008, 27-32 (in Russian)

Mudrik, J.-Liptak, N.-Nad', M. The effect of the speed-torque characteristics upon the steady-state motion of the machine aggregate. In Proceedings of the X. International Conference on the Theory of Machines and Mechanisms, Liberec, 2008, 417-422

Nad', M. Structural dynamic modification of vibrating systems. Applied and Computational Mechanics, 2007, 203-214

Oravcova, J., Mudrik, J. Contribution to dynamics of machine aggregates containing gearing. Acta Mechanica Slovaca, TU Kosice, 2008, 3, 317-324

Mudrik, J., Nad', M. Mechatronical approach to machine dynamics. In Proceedings of 10th International Symposium on Mechatronics. Alexander Dubcek University of Trencin, Trencianske Teplice, 2007, 33-38

Tab. 1. Measurement of static moment characteristics of
asynchronous motor at speed 720 [min.sup.-1]

No. [n.sub.d] = 750 [[min.sup.-1]]

 [M.sub.d] [N m] [n.sub.d] [min.sup.-1] s

1 11,40 0 1
2 12,10 75 0,90
3 12,80 150 0,80
4 13,70 225 0,70
5 14,40 300 0,60
6 15,10 375 0,50
7 15,40 450 0,40
8 15,50 465 0,38
9 15,30 525 0,30
10 13,90 600 0,20
11 9,80 675 0,10
12 6,80 712.5 0,05
13 5,03 720 0,04

Tab. 2. Measurement of static moment characteristics
of asynchronous motor at speed 1450 [min.sup.-1]

No. [n.sub.d] = 1 450 [[min.sup.-1]]

 [M.sub.d] [N m] [n.sub.d] [[min.sup.-1]] s

1 11,18 0 1
2 11,85 75 0,95
3 12,22 150 0,90
4 12,64 225 0,85
5 12,95 300 0,80
6 13,58 375 0,75
7 13,94 450 0,70
8 14,25 525 0,65
9 14,73 600 0,60
10 15,15 675 0,55
11 15,67 750 0,50
12 16,13 825 0,45
13 16,32 900 0,40
14 16,51 975 0,35
15 16,61 1050 0,30
16 16,51 1125 0,25
17 15,46 1200 0,20
18 14.00 1275 0,15
19 11,39 1350 0,10
20 7,1 1425 0,05