## An Introduction to Vibration

Foreword by the Author

This booklet attempts to explain in relatively simple terms a complex subject. I have tried to avoid terms that complicate the description and also to avoid mathematics which only prove that it is so but do not explain why.

The purist may find it a little oversimplified, but hopefully the beginner will find it understandable.

Richard Baker

1995

INTRODUCTION

Vibration testing is a subject which on first inspection may seem simple and straightforward. However, you will find that the subject is vast; requiring many skills and experience. This booklet should provide you with a general understanding of the subject and give you an awareness of some of the pitfalls you may encounter.

To perform a vibration test you require three main items:

• The vibration test system
• The vibration test specification
• The item to be tested
The vibration test system

As with any test equipment, the vibration test system with which you are provided has operational limitations; for example, a maximum rated travel. This is only one of many limitations that must be considered before performing any test. If the operational limitations of the vibration system are exceeded, a shorter system life can be expected. In simple terms, it's just like a car, the harder you drive it the more maintenance it will require. It is therefore essential that you know and understand the limitations of your system.

The vibration test specification

There are probably thousands of vibration test specifications. However, the question should always be asked: Is this the correct test for the product and will it test the product satisfactorily? All tests should be questioned, as there is a high probability that it may over-test or under-test the product in question.

The item to be tested

The test item must be fixed to the vibration table. This is done using a fixture (jig). The fixture must transfer the vibration from the table to the test item without adversely influencing the test. Although this may seem simple, it is not. Time and consideration must be given to the fixture design. The vibration that is transferred to the test item must be measured and controlled. The measurement is usually done using one or more accelerometers, but where and how the accelerometers are placed is critical and must form part of a control strategy.

WHY VIBRATION TEST?

Consumers expect and demand products of high quality and reliability. To fulfil these requirements we must consider vibration, since at some time in its life the product will be subjected to vibration. Poor mechanical design will result in mechanical failure and customer dissatisfaction which will add cost and reduce credibility.

Some reasons for Vibration Testing

• Reduce product development time
• Ensure new products are fit for purpose
• Reduce in-plant rework due to QA rejection
• Reduce damage in transit and subsequent rejection by the customer
• Reduce marginal or non-performance rejection under Warranty
• Reduce legal costs and damage claims due to incorrect operation of the product
• Maintain a good reputation for the company and its products
• Maintain profit margins
In a highly competitive world marketplace Vibration Testing makes good sense.

WHAT IS A VIBRATION TEST SYSTEM?

The essential components of a vibration test system are:

• Vibrator (sometimes referred to as the Shaker or Exciter)
• Amplifier
• Controller
• Accelerometer

HOW DOES A VIBRATOR WORK?

In principal the electrodynamic vibrator operates like a loudspeaker, where the movement of the coil (armature) is produced by an electrical current in the coil which produces a magnetic field opposing a static magnetic field. The static magnetic field is produced by a permanent magnet in small vibrators and an electromagnet in large vibrators. The electromagnet is a coil of wire which is commonly referred to as the field coil.

The force that the coil (armature) can produce is proportional to the current flowing in the coil. To calculate the force produced, the following formula can be applied.

F = B I L Where:

• F = force [Newton] [N]
• B = magnetic flux density [Tesla] [T]
• I = current [Amp] [A]
• L = length [metre] [m]

Other considerations

To design a vibrator whose armature will go up and down is a relatively simple process.

The major part of the design process will ensure that:

• The rotational and cross axial motion is kept to a minimum
• The armature is as light and as strong as possible
How vibration test equipment manufacturers achieve these design requirements is beyond the scope of this booklet but needless to say, experience, knowledge and access to the latest design tools plays a major part.

WHAT DOES THE AMPLIFIER DO?

The purpose of the amplifier is to provide power to the vibrator's armature coil. The power is in the form of voltage and current. In simple terms the more velocity (armature speed) that is required the greater voltage swing will be required. Likewise, the more force or acceleration that is required the more current will be needed.

• Velocity is proportional to Voltage
• Force is proportional to Current
• Acceleration is proportional to Current

An LDS SPA10K 10 kVA amplifier has an maximum voltage output of 100 volt rms and will provide 100 amps rms current, i.e. 100 volts x 100 amps = 10000 VA (10kVA).

The voltage gain of the amplifier is 100, which means that for an input of 1 volt rms the output would be 100 volts rms, but the output voltage could be expressed as:

100 volt rms = 141.4 volt peak = 282.8 volt peak to peak

The above is derived from the fact that the relationship between the rms and the peak value of a sine wave is the square root of 2 (1.414213562). This relationship is known as the crest factor.

But for random operation it is necessary to have a current crest factor of 3, that is the ratio of the rms value to the peak value should be 3. Therefore the amplifier should have a peak current capability of 3 times its rms value.

Thus for a SPA10K amplifier although the maximum rms current is 100 amps, its peak current capability is 300 amps.