Use of electrical oscillating circuit for mechanical resonance simulation of a real shaker system

A lot of products and devices undergo tests for resistance to various vibration impacts. Technocratic society development leads to growth of manufacturing spectrum and scale thus constantly increasing the need for vibration tetsting equipment. For the purpose of vibration tests automation special vibration test control systems are developed. In the course of vibration tests we face resonance caused by shaker system, shaker plate and the tested object. No matter what the resonance source is, shaker control system should provide the set profile parameters within the set tolerance values. Since there are a lot of shaker control systems, let us consider their characteristics – one of them is the signal maintenance within the tolerance range (6 dB) for the resonance with high reactance factor. Use of reference shaker system for the purpose of comparing this parameter of two differenet shaker systems implies considerable material and organization expenses. Since the shaker control system receives data not from the shaker system itself, but from different vibration sensors, transmitting mechanical oscillations into electrical signals, one can use electrical oscillating circuit in order to simulate the resonance. This option is inexpensive and easy to implement since the theoretical aspects have been thoroughly studied and the necessary elements are easily available.

Circuit diagram of sequential electrical oscillating circuit 

Electrical oscillating circuit resonance frequency:

Electrical oscillating circuit reactance factor:

Diagram of capacitor voltage dependence on frequency

The figure above depicts a diagram of capacitor voltage dependence on frequency with a typical resonance crest factor. To determine resonance sharpness one should estimate oscillating circuit reactance factor. For electrical oscillating circuit the reactance factor is determined as a ratio of circuit wave impedance to the resistive voltage; or as a ratio of resonance frequency voltage to zero frequency voltage (i.e. to that of power supply source). For mechanical and electromechanical systems resonance reactance factor can be estimated only by an experimental approach.

The higher is the oscillating circuit reactance factor, the sharper and higher will be the resonance (hence, it will be more difficult for the shaker control system to maintain the signal within specified range, since at a constant sweep speed the shaker system transmission ratio changes faster).

Diagrams of resonances having different reactance factors

The figure above shows electrical oscillating circuits diagrams having the same resonance frequency and different reactance factor parameters. It is possible to vary the electrical oscillating circuit reactance factor by means of adjusting the active resistance value without changing any of the reactive components (i.e. impedance coil and capacitor). The higher is resistor resistance, the lower will be circuit reactance factor, ans vice versa – the lower is resistor resistance, the higher will be circuit reactance factor. It is impossible to achieve ultimate reactance factor value simply by excluding the resistor, since impedance coil wiring has its own active resistance.

Oscillating circuits resonance frequencies (Hz)

10 mH 12 mH 15 mH 18 mH 20 mH 22 mH
0,10 µF 5032,9 4,594,4 4,109,4 3,751,3 3558,8 3393,2
0,22 µF 3393,2 3097,5 2770,5 2529,1 2399,4 2287,7
0,33 µF 2770,5 2529,1 2262,1 2065,0 1959,1 1867,9
0,47 µF 3231,5 2119,2 1895,5 1730,4 1641,6 1565,2
0,56 µF 2126,8 1941,5 1736,5 1585,2 1503,9 1433,9
0,68 µF 1930,0 1761,9 2575,9 1438,6 1364,7 1301,2
1,00 µF 1591,5 1452,9 1299,5 1186,3 1125,4 1073,0
1,50 µF 1299,5 1186,3 1061,0 986,6 918,9 876,1
1,80 µF 1186,3 1082,9 968,6 884,2 838,8 799,8
2,20 µF 1070,0 979,5 876,1 799,8 758,7 723,4
2,70 µF 968,6 884,2 790,8 721,9 684,9 653,0
3,30 µF 876,1 799,8 715,3 653,0 619,5 590,7
3,90 µF 805,9 735,7 658,0 600,7 569,9 543,3
4,70 µF 734,1 670,2 599,4 547,2 519,1 494,9

Oscillating circuit reactance factor (at R=1Ohm)

10 mH 12 mH 15 mH 18 mH 20 mH 22 mH
0,10 µF 316,23 346,41 387,30 424,26 447,21 469,04
0,22 µF 213,20 233,55 261,12 286,04 301,51 316,23
0,33 µF 174,08 190,69 213,20 233,55 246,18 258,20
0,47 µF 145,86 159,79 178,65 195,70 206,28 216,35
0,56 µF 133,63 146,39 163,66 179,28 188,98 198,21
0,68 µF 121,27 132,84 148,52 162,70 171,50 179,87
1,00 µF 100,00 109,54 122,47 134,16 141,42 148,32
1,50 µF 81,65 89,44 100,00 109,54 115,47 121,11
1,80 µF 74,54 81,65 91,29 100,00 105,41 110,55
2,20 µF 67,42 73,85 82,57 90,45 95,35 100,00
2,70 µF 60,86 66,67 74,54 81,65 86,07 90,27
3,30 µF 55,05 60,30 67,42 73,85 77,85 81,65
3,90 µF 50,64 55,47 62,02 67,94 71,61 75,11
4,70 µF 46,13 50,53 56,49 61,89 65,23 68,42

Example of electrical oscillating circuit 

Oscillating circuit nominal parameters: C=0.19 µF, L=18 mH, RL=15.5 Ohm, R=0 Ohm, f=2721 Hz, Q=18,6.

Real oscillating circuit measured frequency response 

The figure above shows real electrical oscillating circuit frequency response based on the above parameters. Software application for measuring frequency responce is available in the “Metrology” tab of ZETLAB control panel and is included into basic configuration.

Measured oscillating circuit parameters are as follows: f=2770 Hz, Q=15

Resonance maintenance: shaker control system  SinVibration «ZETLАВ»


Resonance transmission

The figure above shows printscreen of vibration system control program “SinVibration”, multichannel oscillograph and multichannel recorder windows. Oscillograph and recorder windows depict generator’s voltage. Shaker control system depicts the set vibration test profile and signal diagram via the feedback channel.

Set profile

  • initial point 1000 Hz 1g ,
  • end point 5000 Hz 1g.
  • sweep speed 10 oct/min,
  • maximum tolerance ±6 dB.

Resonance maintenance with reactance factor 15 at the speed of 10 oct/min 

Resonance maintenance with reactance factor 15 at the speed of 1 oct/ min

See also: Methods of electrical oscillating circuit reactance factor evaluation.

The article has been published in the magazine «Industrial automation» № 11, 2010

Author: Begishev S. V.

References cited:

«Electrotechnics», Usoltsev A. A.

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