Foundation for Vibration Measurements

1) History of Vibration Measurements

a. Test: Since the mid to late 1950's the Aerospace and Automotive industries have performed vibration tests and measurements as part of their design process.

a. Predictive Maintenance: Since the end of the 1960's vibration measurements have been routinely taking on critical and expensive machinery for the purpose of minimizing both downtime and maintenance repair costs.

b. Marine: The Society of Navel Architects and Marine Engineers (SNAME) has several Technical Committees that address vibrations two are:

i. Ships Machinery, M-20 Machinery Vibrations

ii. Hull Structures, HS-7 Vibrations

c. The cost of vibration sensors has decreased significantly with recent technological improvements in their production process and computer power continues to increase while their costs decrease.

d. The knowledge base for conducting and analyzing vibration measurements continues to increase, while also crossing industry lines.

2) Tools used

a. Accelerometers - At the foundation of measuring vibration is a sensor (accelerometer) that transforms a mechanical motion into a usable electrical signal. Accelerometers come in hundreds of shapes, sizes and sensitivities, but operate on the same basic principal, Newton's second law F=ma (Force =mass X acceleration) which can be expressed as F/m=a. An accelerometer consists of a small internal mass acting on a piezoelectric element. When it is excited by an external force it produces an electrical output proportional to acceleration, thus accelerometer.

b. Vibration Meters are the simplest and least expensive means of obtaining a vibration measurement. A handheld vibration meter can give an indication of the vibration's severity even if the vibration is not physically evident. Utilizing this information the user has an early warning of an impending problem. They can monitor a vibration induced by a mechanical fault, a damaged coupling, or bent shaft. Corrective action can then be taken before eventual damage occurs. A handheld meter can also be used for acceptance testing, to determine if something falls within acceptable limits.

i. Vibration meters are the most basic means of obtaining a measurement. They provide an overall measurement, meaning they are looking at all the energy within a specified frequency range.

ii. They display this information in RMS [ Root Mean Squared √((v₁²+ v₂²+v₃²+v₄²+ v_n²)/n) ], which is a measure of the energy content of the vibration signal.

iii. In addition to providing a quantifiable value of a vibration, vibration meters can be used for Trending and Acceptance Tests.

1. Trending - periodic plotting and comparison of a monitoring measure over time.

2. Acceptance test can be performed to see if something falls within a specific level. These levels can be based on a purchase specifications, established guidelines, derived from severity charts, or can be established from a known source.

Blake Chart ISO 10816

c. Oscilloscope - One of the first electronic devises used to view vibration, an oscilloscope displays the complex vibration signal produced by the sensor. The display is amplitude versus time and is sometimes referred to as the time domain of a vibration signal.

d. Spectrum Analyzers - To perform sophisticated vibration analysis we must breakdown the complex waveform into its individual components. The display is amplitude versus frequency and is sometimes referred to as the frequency domain of a vibration signal.

i. The Fourier Transformation - French mathematician John Baptiste Fourier (1768-1830) discovered that all complex harmonic signals can be broken down into a series of simple sine waves, with each having different amplitudes and frequencies. When the individual sine waves are combined, or added together, the complex signal is reconstructed.

1. Everything is in Hz or CPS (Cycles Per Second), 1 Hz = 60 CMP (Cycles Per Minute), 1 CPM = 1 RPM.

ii. In 1965 J.W. Cooley and J. W. Tukey, of Columbia University, created an algorithm capable of rapidly calculating the Fourier Transformation. When used on a computer, the FFT (Fast Fourier Transformation) is one of the most powerful tools that we have for analyzing vibration.

Fundamentals of Vibration

1) Vibration is an oscillatory motion from an equilibrium point in response to a force, often called excitation. Examples of a potential force may be mass unbalance and misalignment. The process is one of cause and effect and the magnitude of vibration is dependent not only on the force but also on the properties of the system (mass, stiffness and damping), both of which may depend on speed.

2) The three fundamental characteristics of vibration are Frequency, Amplitude and Phase. We have already discussed frequency. Amplitude is the maximum value of vibration at a given location on a machine or structure and we will discuss phase shortly.

3) Measurement Types and how they are derived

a. There are three ways that we can look at the sensors output: Acceleration (g's), Velocity (in/sec) and Displacement (mils). An accelerometer's output is in g's (Acceleration); if we perform the mathematical function of integration to the acceleration signal we can obtain a Velocity signal. If we integrate the Velocity signal (double integration of acceleration) we can obtain a Displacement signal.

i. Why three types of measurements? Because of the mathematical computations one type of measurement may be better suited than another.

1. Displacement emphasizes the lower frequencies and de-emphasizes those that are higher. Conversely Acceleration emphasizes the higher frequencies and de-emphasizes those that are lower.

a. Displacement is useful from 0 - 20 Hz.

b. Velocity is useful from 10 - 1,000 Hz.

c. Acceleration is useful for > 1,000 Hz.

2. We cannot start with Displacement and differentiate (the inverse of integration) to Velocity and then differentiate again to Acceleration because the electronic circuitry required to perform the derivations induces noise. This is one of the reasons accelerometers are the sensor of choice for vibration measurements.

4) Relationship of Acceleration, Velocity, and Displacement

a. Acceleration is the time rate of change of Velocity and Velocity is the time rate of change of Displacement.

b. Forces are the cause of vibration. The force is the first event that occurs in time. The response to these forces are movements. The movements can be described as displacement, velocity, or acceleration. Displacement is how we normally perceive motion; however, velocity and acceleration are also valid descriptive quantities for mechanical motion. The displacement, velocity, or acceleration are all responses to some force. The force leads the response in time. The force occurs first, the movement occurs later, i.e., there is a phase lag between the force and the response. In addition there is a 90� phase difference between displacement and velocity, and a 180� phase lag between displacement and acceleration.

5) Phase can be used to determine the time relationship between an excitation (force) and the vibration it causes; for example, the force due to mass unbalance and the vibration it causes.

6) Resonance and Natural Frequency

a. Natural frequencies are determined by the design of a system or structure and are dependent on mass, stiffness and damping.

b. Every physical object has a natural frequency and it is the frequency that it will oscillate at if excited by a force. Objects absorb energy at their natural frequencies. Therefore, depending on damping, the resulting vibration amplitude can be magnified 10 to 100 times.

c. Resonance is a condition that results in the amplification of vibration when the forcing frequency is close to or at a natural frequency.

Masses move readily at low frequencies, so below resonance the system is stiffness dominant. Above resonance, the mass inertia of the system becomes dominant. Since masses don't like to move at higher frequencies, most of the force input is consumed in overcoming inertia of the system. The force due to stiffness kx is not dependent on frequency. Therefore, the stiffness force is constant with frequency. The force due to inertia is proportional to acceleration and increases with frequency in a quadratic manner. Below a natural frequency the inertia force and the stiffness force are always 180� out of phase. The magnitude of the inertia force increases with frequency and at some point it equals the stiffness force magnitude. When this occurs, there are two force of equal magnitude and 180� apart. They essentially cancel each other, and we have a situation with a driving force input and no restraints...this is a condition of resonance.

d. Critical Speed is the rotational speed corresponding to a natural frequency of a rotating shaft or system.

e. The wine glass is a perfect example of resonance and natural frequency.

1. If you strike the glass with your fingernail it will ring. This is because an impulse force excites all frequencies.

2. If you run your wet finger around the rim you are hunting for the natural frequency.

3. The singer breaking the class is an example of the amplification of vibration.

f. Back to Phase, in particular Phase Shift and its relationship with resonance.

1. Of interest is the affect concerning a rotational element. When approaching resonance, or critical speed, the vibration increases. It peaks at the critical speed and smoothes out at higher speeds. The reason for this is because of a 180� phase shift at resonance. The response to a force (imbalance) is delayed 180� which causes the mass center to be pulled in closer to the center of rotation.

2. This is of particular interest because you will be unable to balance a rotational element at or near its resonance.

7) Measurement location and considerations in mounting a sensor. The method used to mount a vibration sensor can affect its frequency response.

The location is equally as important. If you are measuring the vibration of a rotational element you should be as near perpendicular to the centerline axis as possible.