## Introduction

Nearly all vibration tests cover a frequency range where mechanical resonances occur in a system consisting of payload, fixture and armature. In this context, the test is controlled by acceleration, based on the following basic equation at constant mass:

force = mass × acceleration (f = ma)

However, under resonance conditions, the effective mass does not remain constant. Therefore, poor vibration control can lead to underloading or overloading of the payload and damage due to overdriving of the armature. Choosing where to place the control accelerometers is one of the most critical parts of any vibration test.

There are no universally suitable active vibration control positions. Nevertheless, the wrong positions can damage the vibration equipment or affect the accelerations applied to the payload. The following principles should therefore be observed:

• All mechanical structures have resonances
• The larger a structure, the lower the resonant frequency
• For increased mass without increased stiffness, the resonant frequency will reduce
• For increased stiffness without increased mass, the resonant frequency will increase
• In a free system, when a purely axial resonance occurs, the liveliest points will always be the ends

## Choosing the Control Position

The most obvious reason for control accelerometers is to limit the acceleration into the payload. If the payload is large and/or the frequency range is high, at some point one or more resonances will occur. This can be seen as the difference in acceleration levels over the fixture.

If only one accelerometer position is used in a test, the control loop ensures control of acceleration at that position only. If this position coincides with a resonance node where there is little or no motion, the rest of the structure can be accelerated by more than a hundred times the control value.

To determine if a control accelerometer is attached to a node, a look at the drive signal, showing the dynamics of the system, provides clarity. A decrease in the drive indicates resonance, and an increase in the drive indicates anti-resonance. In case of anti-resonance, the control positions should be changed. Examples of good and bad drive plots are shown in the figure below.

As the location of nodes changes with frequency, finding a point where they will not occur is difficult. It is for this reason that several accelerometer positions should be used. The best area to place accelerometers, with least risk of finding a node, is at the end of the system. If this is not possible, the monitors should be adjusted with notching levels so that the vibrator is not damaged.

## Random vs Sine Testing

There is a difference between the control system of a shaker in sine and random testing.

### Sine Testing

The amplifier monitors the voltage and current supplied to the shaker, stopping the test if either exceeds the preset trip levels. In case of a high-level test, and if the control position is at a node, the drive power may increase above the trip level, causing the system to shut down.

### Random Testing

The amplifier monitors RMS voltage and current in a similar manner. If the control position is at a node, the amplifier will not shut down if the total voltage and current remain below the trip level. This remains true even though the shaker may be producing more force than required.

A further complication is that, at the resonant frequency of the armature itself, there is a large amount of ‘free energy’. Little voltage and current is required to drive the armature at this frequency. It is possible to damage the armature by overdriving the shaker without causing amplifier shutdown. Placing a control accelerometer at the end of the system protects against this danger, since it moves in a similar way to the armature at the other end.

## The Best Practice for Your Control Strategy

Following good practice as described below will maximize the life of the equipment:

1. Always attach an accelerometer to the end of the system to either control or monitor it. Set the limits to the maximum theoretical acceleration using the calculation f = ma.
2. Large slip tables may require several control accelerometers positioned at the end. The corner of the plate will be vibrating at a different level to the centre, and at higher frequencies.
3. Run low-level sine sweeps over the entire testing frequency range to characterize the fixture and payload. This could be low-level random if sine is prohibited. Low level means approximately –12 dB of the full test level.
4. Review the drive to ensure there are no rises past the nominal drive level.
5. Use the results to modify the control strategy if required.
6. Pay attention to the energy outside the frequency band during random operation. The bandwidth should be at least 1.5 times the highest control frequency.
7. If this energy is large or at the same level as the controlled energy, an investigation should be made before proceeding.
8. If problems occur, look at the real-time acceleration recording. This may reveal problems that are not visible in the frequency domain.
9. If everything is fine, proceed to the test level.

This will protect the shaker from damage as much as possible. If these precautions are not taken, the shaker will be forced to deliver more than the intended force or acceleration levels, shortening its life.